Answer: the wire should be cut into 12 cm and 28 cm
Step-by-step explanation:
All sides of a square is equal.
The perimeter of a square is the distance around the square.
Let L represent the length each side of one of the squares. Then the perimeter of this square is 4L.
The length of a side of one square is to be 4 longer than length of a side of the other. This means that the length of each side of the other square is L + 4
The perimeter of the other square would be 4(L + 4) = 4L + 16
Since the piece of wire is 40 cm long, then
4L + 4L + 16 = 40
8L = 40 - 16 = 24
L = 24/8 = 3
The perimeter of the first square is
4L = 4 × 3 = 12
The perimeter of the second square is
4L + 16 = 4 × 3 + 16= 28
Final answer:
To make two squares with one side being 4 cm longer than the other, a 40 cm wire should be cut into pieces of 12 cm and 28 cm.
Explanation:
The question concerns cutting a 40 cm long piece of wire into two pieces to form two squares, where the length of a side of one square is 4 cm longer than the length of a side of the other square. Let's denote the length of the side of the smaller square as x cm. Thus, the side of the larger square will be x + 4 cm. Since the perimeter of a square is four times its side length, the total length of wire used for the smaller square will be 4x cm, and for the larger square will be 4(x + 4) cm.
Combining the total length of both squares, we have:
4x + 4(x + 4) = 40
This simplifies to:
8x + 16 = 40
Subtracting 16 from both sides, we get:
8x = 24
Dividing both sides by 8, we find:
x = 3
Therefore, the side of the smaller square is 3 cm, and the side of the larger square is 7 cm. To find out how long each piece of wire must be cut, we calculate the perimeters:
Smaller square wire length: 4(3) = 12 cm
Larger square wire length: 4(7) = 28 cm
So the wire should be cut into one 12 cm piece and one 28 cm piece.
A power plant is located on a river that is 600 feet wide. To lay a new cable from the plant to a location in a city 1 mile downstream on the opposite side costs $175 per foot across the river and $100 per foot along the land. Suppose that the cable goes from the plant to a point Q on the opposite side that is x feet from the point P directly opposite the plant. Write a function C(x) that gives the cost of laying the cable in terms of the distance x. 1 mi city Cl 600 ft power plant
Answer:
C(x) = 175√(x² + 360000) + 528000 - 100x
Step-by-step explanation:
See the attachment below (Line PR = 1mile)
C(x) = Cost of Distance across the river + Cost of Distance along the land
Calculating Distance Across the river:
In triangle OPQ,The distance across the river is represented by line y
Line y is the hypothenus of the triangle
Pythagoras theorem states that:
if one angle of a triangle is 90 degrees, then the square of the length of the hypotenuse - the side opposite the right angle - is equal to the sum of the squares of the lengths of the other two sides.
So,
y² = x² + 600²
y² = x² + 360000
y = √(x² + 360000)
If it costs $175 per foot across the river then It'll cost
175 * √(x² + 360000) to lay cables across the river.
Calculating Distance along the land
Distance along the land is represented by line QR
Line QR = Line PR - PQ.
Where PR = 1 Miles (1 mile = 5280 feet)
So, PR = 5280
Line PQ = x
So, QR = 5280 - x
If it costs $100 per foot along the land,then it'll cost
100 * (5280 - x) to lay cables along the land
= 528000 - 100x
C(x) = 175√(x² + 360000) + 528000 - 100x
What is the difference in area covered by a single 3 inch windshield wiper operating with a central angle of 138 degrees compared to a pair of 5 inch wipers operating together each having a central angle of 114 degrees?
Answer:
38.9 square inches.
Step-by-step explanation:
We are asked to find the difference in area covered by a single 3 inch windshield wiper operating with a central angle of 138 degrees compared to a pair of 5 inch wipers operating together each having a central angle of 114 degrees.
We will use area of sector formula to solve our given problem as:
[tex]\text{Area of sector}=\frac{\theta}{360}\times \pi r^2[/tex], where, r represents radius and theta represents central angle.
Let us find area of sector with central angle 140 degree and radius 3 inch.
[tex]\text{Area of sector}=\frac{138}{360}\times \pi (3)^2[/tex]
[tex]\text{Area of sector}=\frac{138}{360}\times 9\pi[/tex]
[tex]\text{Area of sector}=10.83849[/tex]
Now, we will find area of sector with central angle 114 degree and radius 5 inch and multiply by 2 as:
[tex]\text{Area of sector}=2(\frac{114}{360}\times \pi (5)^2)[/tex]
[tex]\text{Area of sector}=2(\frac{114}{360}\times 25\pi)[/tex]
[tex]\text{Area of sector}=\frac{114}{360}\times 50\pi[/tex]
[tex]\text{Area of sector}=49.74188[/tex]
Let us find difference of area as shown below:
[tex]\text{Difference of areas}=49.74188-10.83849[/tex]
[tex]\text{Difference of areas}=38.90339[/tex]
[tex]\text{Difference of areas}\approx 38.9[/tex]
Therefore, the difference in area covered is approximately 38.9 square inches.
Final answer:
Calculate the areas covered by differently sized and angled windshield wipers to find the difference.
Explanation:
Single 3-inch wiper:
Area covered = (1/2) × r² × (2 × pi × (angle/360))Pair of 5-inch wipers:
Each wiper's area = (1/2) × r² × (2 × pi × (angle/360))Total area covered by the pair = 2 × (area of a single wiper)The difference in area cleaned by the pair of 5-inch wipers compared to the single 3-inch wiper is:
A-diff = A-combined - A-single ≈ 31.50 sq in - 7.07 sq in ≈ 24.43 sq in
Therefore, the pair of 5-inch wipers cleans approximately 24.43 square inches more area than the single 3-inch wiper.
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠R.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠R = °
Answer:
[tex]m\angle R=69.4^o[/tex]
Step-by-step explanation:
we know that
In the right triangle PQR
[tex]tan(R)=\frac{PQ}{QR}[/tex] ----> by TOA (opposite side divided by adjacent side)
substitute the given values
[tex]tan(R)=\frac{8}{3}[/tex]
using a calculator
[tex]m\angle R=tan^{-1}(\frac{8}{3})=69.4^o[/tex]
What is the sum of the geometric series? Sigma-Summation Underscript n = 1 Overscript 4 EndScripts (negative 2) (negative 3) Superscript n minus 1
Answer:
Step-by-step explanation:
∑⁴ₙ₌₁ -144 (½)ⁿ⁻¹
This is a finite geometric series with n = 4, a₁ = -144, and r = ½.
S = a₁ (1 − rⁿ) / (1 − r)
S = -144 (1 − (½)⁴) / (1 − ½)
S = -270
If you wanted to find the infinite sum (n = ∞):
S = a₁ / (1 − r)
S = -144 / (1 − ½)
S = -288
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Answer:
The answer is C (40)
Step-by-step explanation:
A license plate consists of seven symbols on each plate, where the first two symbols are letters of the alphabet and the following five symbols are the digits selected from the set StartSet 0 comma 1 comma 2 comma 3 comma 4 comma 5 comma 6 comma 7 comma 8 comma 9 EndSet? How many license plates can be produced if any digit or letter can be repeated on any given license plate?
Final answer:
To find the total number of possible license plates with two letters followed by five digits (with repetition allowed), multiply the number of options for each position: 26 letters and 10 digits result in 67,600,000 different license plates.
Explanation:
The question asks for the total number of license plates that can be produced when the first two symbols are letters from the alphabet and the following five symbols are digits from 0 to 9, with repetition allowed for both letters and digits. To find the number of possible license plates, we use the principle of counting, multiplying the number of choices for each position.
There are 26 possible letters for each of the first two positions (since there are 26 letters in the English alphabet) and 10 possible digits (0-9) for each of the last five positions.
Therefore, the total number of license plates that can be created is calculated as:26 * 26 * 10 * 10 * 10 * 10 * 10. This equals 67,600,000 possible license plates.
This calculation assumes that each symbol (letter or digit) can be repeated, meaning the same letter or digit can be used more than once in the license plate.
A seven-year medical research study reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug.a. This study involved the comparison of two populations. What were the populations?b. Do you suppose the data were obtained in a survey or an experiment?c. For the population of women whose mothers took the drug DES during pregnancy, a sample of 3980 women showed 63 developed tissue abnormalities that might lead to cancer. Provide a descriptive statistic that could be used to estimate the number of women out of 1000 in this population who have tissue abnormalities.d. For the population of women whose mothers did not take the drug DES during pregnancy, what is the estimate of the number of women out of 1000 who would be expected to have tissue abnormalities?e. Medical studies often use a relatively large sample (in this case, 3980). Why?
Answer:
16 women per 1 000
Step-by-step explanation:
The data was likely to be obtained from a survey. The question states how the information was gathered - most probably from questionnaires.
c. A simple model will be 16 women per 1 000 women. Proportion has been taken into account here.
Let 63 correspond with those that are going to get cancer out of 3980. The women have 63/3980 chance of getting cancer.
For 1 000 women that will be 1000/3980 × (63) = 16
Therefore the probability of a person getting cancer is 16 per 1 000 Ans
e. Large samples are essential to ensure that the results are representative of the actual population. In addition, large samples reduce inherent errors from deviations. Furthermore, useless data can be discarded and the remaining data still represent the actual population size. Lastly, large amounts of data are easy to scale up and use to develop models.
The two populations compared in the study were women whose mothers took the drug DES during pregnancy and those whose mothers did not. The data in the study were obtained through an observational study. A descriptive statistic can be used to estimate the number of women with tissue abnormalities out of 1000 in the population of women whose mothers took the drug DES during pregnancy.
Explanation:a. The two populations in the study were: 1) women whose mothers took the drug DES during pregnancy and 2) women whose mothers did not take the drug.
b. The data in this study were obtained through an observational study, specifically a cohort study. This means that the researchers observed and compared the outcomes between the two groups of women without directly manipulating any variables.
c. A descriptive statistic that could be used to estimate the number of women out of 1000 in the population of women whose mothers took the drug DES during pregnancy and developed tissue abnormalities is:
Number of women with tissue abnormalities in the sample: 63
Descriptive statistic: (63 / 3980) * 1000 = 15.83
Therefore, an estimate is that 15.83 out of 1000 women in this population have tissue abnormalities that might lead to cancer.
d. Since the study only reported that women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities, without providing an exact percentage, it is not possible to estimate the number of women without more specific information.
e. Medical studies often use a relatively large sample size, like 3980, to increase the reliability and representativeness of the findings. A larger sample size helps to reduce the chance of biased or random results and increases the generalizability of the findings to the larger population.
The ratio pv to nrt is plotted against pressure for ch4 at 0°c and 200°c. why does the curve for 0°c drop below the horizontal line for an ideal gas whereas the curve for 200°c does not?
Answer:
See answer below
Step-by-step explanation:
the ratio of pv against nrt is called compressibility Z and measures the deviation from an ideal gas behaviour . When Z is plotted against pressure for CH₄ for 0°C and 200°C the curves will differ because there are
- negative deviations ( Z decreases) due to intermolecular forces
- positive deviations (Z increases ) due to molecular size of gas particles
then
- at 0°C the negative deviations prevail respect to positive deviations at lower pressures ( so Z drops below the horizontal line first ) and then Z increases when pressure increases since the effect of positive deviation is higher ( then Z increases)
- Nevertheless, at 200°C the effect of intermolecular forces is lower and thus the positive deviations always prevail ( thus you observe only Z increasing(
Use a sample n=1400 , p=0.20 and a 99% confidence level to construct a confidence interval estimate of the population proportion, p
Answer:
[tex]0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172[/tex]
[tex]0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228[/tex]
The 99% confidence interval would be given by (0.172;0.228)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The population proportion have the following distribution
[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]
If we replace the values given we got:
[tex]0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172[/tex]
[tex]0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228[/tex]
The 99% confidence interval would be given by (0.172;0.228)
The confidence interval for the proportion is CI = 0.20 ± 0.0275.
Confidence intervalThe formula for calculating the confidence interval for proportion is expressed as:
[tex]CI=p \pm z \cdot \sqrt{\frac{p(1-p)}{n} }[/tex]
where:
p is the proportion = 0.20n is the sample space = 1400z is the z-score at 99% interval = 2.98Substitute into the formula;
[tex]CI=0.20 \pm 2.576 \cdot \sqrt{\frac{0.2(1-0.2)}{1400} }\\CI=0.20 \pm 2.576 \cdot \sqrt{\frac{0.2(0.8)}{1400} }\\CI = 0.20 \pm 0.0275\\[/tex]
Hence the confidence interval for the proportion is CI = 0.20 ± 0.0275.
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Which best describes the three-dimensional figure obtained from rotating the figure around the y-axis?
a cylinder with a radius of 1 unit
a cone with a radius of 1 unit
a cylinder with a radius of 2 units
a cone with a radius of 2 units
Yo sup??
This question can be solved by just imagining the object formed or practically trying it out.
Therefore the correct answer to this question is option 2 ie
a cylinder with a radius of 1 unit.
Hope this helps.
The figure created is a cone with a height of 2 units and a radius of 1 unit.
Which figure will be created?
Notice that we have a triangle, so if we rotate it around the y-axis, we will get a cone.
Because the rotation is around the y-axis, the height of the cone will be equal to the side AB of the triangle, so the height of the cone is 2 units.
And the radius of the cone is equal to BC, then we can see that the radius measures 1 unit.
Then the figure created is a cone with a height of 2 units and a radius of 1 unit.
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Using the piling method, which of the following can be constructed from polygons alone?
Check all that apply.
Answer:
B and C.
Step-by-step explanation:
A prism can be constructed from 4 sided polygons like a rectangle.
A pyramid (not including the vertex) can be constructed from squares of diminishing size.
The piling method allows for the construction of various three-dimensional shapes using polygons alone. Some of the shapes that can be constructed include prisms, pyramids, and cones.
Explanation:The piling method, also known as the additive method or stacking method, allows for the construction of various three-dimensional shapes using polygons alone. Some of the shapes that can be constructed include prisms, pyramids, and cones.
Prisms:
A prism is a three-dimensional shape with two congruent polygonal bases and rectangular lateral faces connecting the corresponding vertices of the bases. Examples of prisms include rectangular prisms (cuboids), triangular prisms, and hexagonal prisms.
Pyramids:
A pyramid is a three-dimensional shape with a polygonal base and triangular faces connecting the vertices of the base to a single point called the apex or vertex. Examples of pyramids include square pyramids, triangular pyramids, and pentagonal pyramids.
Cones:
A cone is a three-dimensional shape with a circular base and a curved surface that connects the base to a single point called the vertex. Cones can be constructed using polygons by approximating the curved surface with a series of smaller polygons.
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What is the median of the following values? 51,22,17,28,98,4,24,83,9,76
Answer:
The answer to your question is 26
Step-by-step explanation:
Median is the middle number of a list order from lowest to highest.
Process
1.- Order the numbers from lowest to highest
4 9 17 22 24 28 51 76 83 98
2.- Look for the middle number, if the total number of items is pair, take the 2 middle number and divide by two.
Middle numbers = 24 and 28
Median = (24 ´+ 28) / 2
Median = 52/2
Median = 26
Answer:
Step-by-step explanation:
First the numbers are arranged in ascending order from the least to the biggest number:
4 9 17 22 24 28 51 76 83 98
The numbers on the 5th and 6th position are in the middle
5th= 24
6th = 28
Since they are two numbers, we add them and divide by 2
= (24 + 28) / 2
= 52 / 2
= 26
Consider the graph of quadrilateral ABCD.
What is the most specific name for quadrilateral ABCD?
square
rectangle
parallelogram
rhombus
Know the properties of each shape:
A square has all sides of equal length plus all corners are right angles
A rectangle has all right angles, but has two pairs of parallel sides
A parallelogram is a quadrilateral that has two pairs of parallel sides
A rhombus is where all sides are equal length, but no right angles at all
So the best choice given the diagram is C: parallelogram
Hope this helped you to understand better.
A solid rectangular box with height 5 m and square base with side lengths 4 m is built using a lightweight material whose density is 800 kgm3. Constructing this box requires work against gravity.the required work is___________
Final answer:
The work done against gravity in constructing the rectangular box is 3136000 J.
Explanation:
To calculate the work done against gravity in constructing the rectangular box, we need to first calculate the mass of the box. The density of the lightweight material is given as 800 kg/m³. Since the base of the box is a square with side lengths of 4 m and the height is 5 m, the volume of the box is V = (4 m)(4 m)(5 m) = 80 m³.
The mass of the box can be calculated using the formula mass = density × volume. Therefore, the mass of the box is [tex](800 kg/m^3)(80 m^3) = 64000 kg.[/tex]
The work done against gravity is given by the formula work = mass × gravity × height. Assuming the acceleration due to gravity is approximately 9.8 m/s², the work done against gravity is [tex](64000 kg)(9.8 m/s^2)(5 m) = 3136000 J.[/tex]
The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it is wide. Find the dimensions of the family room
Answer:
The dimensions of the room are length is 16 feet and the width is 11 feet.
Step-by-step explanation:
Given:
The wards decided to use carpet tiles in the family room. The room has an area of 176 square feet and is 5 feet longer than it is wide.
Now, to get the dimensions.
Let the width be [tex]x.[/tex]
So, the length = [tex]x+5.[/tex]
Area = 176 square foot.
So, we put formula of area to get the dimensions:
Area = length × width.
[tex]176=(x+5)\times x[/tex]
[tex]176=x^2+5x[/tex]
Subtracting boths sides by 176 we get:
[tex]0=x^2+5x-176\\x^2+5x-176=0[/tex]
On solving the equation:
[tex]x^2+16x-11x-176=0\\x(x+16)-11(x+16)=0\\(x+16)(x-11)=0[/tex]
As,
[tex]x+16[/tex] = 0
[tex]x=-16[/tex]
So, we would not take the negative result.
Thus,
[tex]x-11=0\\x=11[/tex]
So, the width = 11 feet.
Now, to get the length by substituting the value of [tex]x[/tex]:
[tex]x+5\\=11+5\\=16[/tex]
The length = 16 feet.
Therefore, the dimensions of the room are length is 16 feet and the width is 11 feet.
The width is 11 feet, and the length is 5 feet longer, making it 16 feet.
To determine the dimensions of the family room, we start by defining the width of the room as w. According to the problem, the length (l) is 5 feet longer than the width, so we can write this as:
l = w + 5
We also know the area of the room is 176 square feet. The area of a rectangle is calculated by multiplying the width and length:
Area = width × length
Therefore, we get the equation:
w × (w + 5) = 176
Expanding this equation gives us:
w² + 5w = 176
We rearrange this into a standard quadratic equation:
w² + 5w - 176 = 0
Now we solve for w using the quadratic formula, w = (-b ± √(b² - 4ac)) / 2a, where:
a = 1b = 5c = -176This gives us:
w = (-5 ± √(25 + 704)) / 2
w = (-5 ± √729) / 2
w = (-5 ± 27) / 2
Which simplifies to:
w = 11 or w = -16
Since width cannot be negative, we have:
w = 11
Then the length l is:
l = 11 + 5 = 16
Therefore, the dimensions of the family room are 11 feet by 16 feet.
A corner store bakery sells cake and pies. The cakes are $5 and the pies are $7. In one day the store sells 15 goods and makes a total of $91. How many cakes did they sell?
Answer:
The answer to your question is it sold 7 cakes.
Step-by-step explanation:
Data
cakes = c = $5
pies = p = $7
total pieces = 15
total sell = $91
Process
1.- Write equations to solve this problem
c + p = 15 ------------ l
5c + 7p = 91 ----------- ll
2.- Solve the system of equations by elimination
Multiply equation I by -5
-5c - 5p = -75
5c + 7p = 91
0 + 2p = 16
Solve for p
p = 16/2
p = 8
3.- Substitute p in equation l to find c
c + 8 = 15
solve for c
c = 15 - 8
c = 7
4.- Conclusion
It sold 7 cakes and 8 pies.
Answer: 7 cakes were sold.
Step-by-step explanation:
Let x represent the number of cakes that were sold.
Let y represent the number of cakes that were sold.
The cakes are $5 and the pies are $7. The store makes a total of $91. This means that
5x + 7y = 91- - - - - - -- -1
The store sold a total number of 15 goods. This means that
x + y = 15
Substituting x = 15 - y into equation 1, it becomes
5(15 - y) + 7y = 91
75 - 5y + 7y = 91
- 5y + 7y = 91 - 75
2y = 16
x = 16/2 = 8
x = 15 - y = 15 - 8
x = 7
A consumer takes out a loan for $500 that charges 10% annual interest. What is the total cost of the loan if the consumer pays it back one year from the date of origination?
Answer:the answer is life
Step-by-step explanation:
well life is life that you need
Answer:
$550 i think
Step-by-step explanation:
2. Mama Bear ate 80% as much porridge as Papa Bear did. Baby Bear ate as much as Mama Bear did. Papa Bear ate 1.2 liters more porridge than Mama Bear did. How much porridge did the three bears eat, in all?
Answer:
15.6 liters
Step-by-step explanation:
Let the porridge eaten by Papa bear be 'x' liters.
Given:
Mama Bear ate 80% as much porridge as Papa Bear did.
Baby Bear ate as much as Mama Bear did.
Papa Bear ate 1.2 liters more porridge than Mama Bear did
So, porridge eaten by Mama Bear = 80% of 'x' = [tex]0.80x[/tex]
Now, Baby Bear eats same amount as Mama Bear. So,
Porridge eaten by Baby Bear = [tex]0.80x[/tex]
Papa Bear ate 1.2 liters more than Mama Bear.
Framing in equation form, we get:
[tex]x = 1.2 + 0.80x[/tex]
[tex]x-0.80x=1.2[/tex]
[tex]0.20x=1.2[/tex]
[tex]x=\frac{1.2}{0.20}=6\ liters[/tex]
So, Papa Bear ate 6 liters of porridge.
Mama Bear ate = 0.80 × 6 = 4.8 liters
Baby Bear ate = 4.8 liters.
So, total porridge = Papa Bear + Mama Bear + Baby Bear
Total porridge eaten = 6 + 4.8 + 4.8 = 15.6 liters
Answer:
Step-by-step explanation:answer is 20%
Which expression is equivalent to -3x - (x-1) + 3/2(3x +3)?
A. 1/2x + 11/2
B. 1/2x + 7/2
c. 5/2x + 11/2
D. 5/2x + 7/2
Answer:
The answer to your question is letter A
Step-by-step explanation:
Expression
- 3x - (x - 1) + 3/2(3x + 3)
1.- Expand
- 3x - x + 1 + 3/2(3x) + 3/2(3)
2.- Simplify
- 3x - x + 1 + 9/2 x + 9/2
3.- Associate like terms
(-3x - x + 9/2x) + (1 + 9/2)
4.- Simplify like terms
(-4x + 9/2x) + (2 + 9)/2
(-8x + 9x)/2 + 11/2
1/2x + 11/2
Where do I share a photo of my work
Sonya is renting a car. She pays a fee of $50 for the rental plus $20 each day she had the car. Suppose she pays a total for $130. For how many days did she rent the car?
Answer: she rented the car for 4 days.
Step-by-step explanation:
Let x represent the number of days for which Sonya rented the car.
She pays a fee of $50 for the rental plus $20 each day she had the car. This means that if she rents the car of x days, the total amount that she would pay is
20x + 50
Suppose she pays a total for $130, it means that the number of days for which she rented the car would be
20x + 50 = 130
Subtracting 50 from the left hand side and the right hand side of the equation, it becomes
20x + 50 - 50 = 130 - 50
20x = 80
x = 80/20 = 4
x squared equals 9 what is the answer
Answer: x = 3
Step-by-step explanation:
x^2 = 9
x = [tex]\sqrt{9}[/tex]
x = 3
Another way to think about it:
We think what number can be multiplied by itself to get 9.
since 3*3=9, our answer is 3
Points R, T, S, and Q are
a. collinear
b. coplanar
c. neither collinear nor coplanar
d. both collinear and coplanar
The points in the diagram are neither collinear (lying on the same line) nor coplanar (lying on the same plane) as some points are not in alignment or on the same level.
The correct answer is option C.
Collinearity and coplanarity are geometric concepts used to describe the relative positions of points in space. To clarify, collinear points lie on the same straight line, while coplanar points lie on the same flat plane.
In your specific scenario, it is evident that the points under consideration do not satisfy the criteria for either collinearity or coplanarity. Here's an expanded explanation:
Collinearity:
Collinear points are points that can be connected by a single straight line. In simpler terms, if you can draw a straight line that passes through all the points without lifting your pen, those points are collinear. However, based on the provided diagram and description, it is clear that not all the points can be connected in this way. Some points are positioned in such a manner that a single straight line cannot pass through all of them.
Coplanarity:
Coplanar points are points that lie within the same flat plane. If you can imagine a flat surface that contains all the points, those points are coplanar. In the given scenario, it is apparent that the points are not all situated within the same plane. Some points are at different heights or elevations compared to others, indicating that they do not lie within a common flat plane.
In conclusion, the points in the diagram do not meet the conditions for either collinearity or coplanarity. They cannot be connected by a single straight line, nor do they all reside on the same flat plane.
Therefore, from the given options the correct one is C.
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Answer:
Step-by-step explanation:
Triangle ABC is a right angle triangle.
From the given right angle triangle
AC represents the hypotenuse of the right angle triangle.
With ∠A as the reference angle,
AB represents the adjacent side of the right angle triangle.
BC represents the opposite side of the right angle triangle.
To determine the ratio of Tan A , we would apply the tangent trigonometric ratio which is expressed as
Tan θ = opposite side/adjacent side. Therefore,
Tan A = 28/45
He drank 2 small bottles and 2 large bottles, for a total of 76 ounces. The day before, he drank 4 small bottles and 1 large bottle, for a total of 83 ounces. How much does each bottle hold?
Answer: the small bottle holds 15 ounces while the large bottle holds 23 ounces.
Step-by-step explanation:
Let x represent the number of ounces that a small bottle holds.
Let y represent the number of ounces that a large bottle holds.
He drank 2 small bottles and 2 large bottles, for a total of 76 ounces. It means that
2x + 2y = 76 - - - - - - - - - - - - 1
The day before, he drank 4 small bottles and 1 large bottle, for a total of 83 ounces. This means that
4x + y = 83 - - - - - - - - - - - - -2
Multiplying equation 1 by 2 and equation 2 by 1, it becomes
4x + 4y = 152
4x + y = 83
Subtracting, it becomes
3y = 69
y = 69/3 = 23 ounces
Substituting y = 23 into equation 1, it becomes
2x + 2 × 23 = 76
2x + 46 = 76
2x = 76 - 46 = 30
x = 30/2 = 15 ounces
Answer:
its 15 and 19 ounces on IXL
Step-by-step explanation:
Find x
1,) -54
2.) 48
3,) 52
4.) 54
Step-by-step explanation:
[tex]m \angle \: WXZ = m \angle \: WYZ \\ ..(angles \: formed \: in \: same \: arc) \\ \therefore \: x \degree = (2x - 54)\degree \\ \therefore \: x = 2x - 54 \\ \therefore \: x - 2x = - 54 \\ \therefore \: - x = - 54 \\ \huge \purple{ \boxed{\therefore \: x = 54}}[/tex]
Answer:
The correct answer is D or 54.
Step-by-step explanation:
A movie studio took a poll after showings of a new movie. The studio found that 5 out of every 24 people did not like the movie. About what percent of the people did not like the movie?
Answer:
= 20.83%
Step-by-step explanation:
5/24 * 100
= 20.83%
To find what percent of people did not like the movie when 5 out of every 24 people did not, we calculate 5/24 as a percentage which is approximately 20.83%, rounded to about 21% of the people.
To calculate the percentage of people who did not like the movie, we need to set up a proportion where the number of people who did not like the movie is to the total number of people. Given that 5 out of every 24 people did not like the movie, we can express this as a fraction: 5/24. To find the equivalent percentage, we set up a fraction with 100 as the denominator and cross-multiply:
5/24 = x/100
Now we cross-multiply and solve for x:
24x = 5imes 100
x = (5 imes 100) / 24
x = 500 / 24
x = 20.833...
This equates to approximately 20.83%, which can be rounded to about 21%. Therefore, about 21% of the people did not like the movie.
1 Suppose you choose at random a real number X from the interval [2, 10]. (a) Find the density function f(x) and the probability of an event E for this experiment, where E is a subinterval [a, b] of [2, 10]. (b) From (a), find the probability that X > 5, that 5 < X < 7, and that X2 − 12X + 35 > 0.
Answer:
Step-by-step explanation:
Given that you choose at random a real number X from the interval [2, 10].
a) Since this is a contnuous interval with all number in between equally likely
E = probability for choosing a real number is U(2,10)
pdf of E is [tex]\frac{1}{8}[/tex]
b) P(X>5) = [tex]\int\limits^10_5 {1/8} \, dx = \frac{5}{8}[/tex]
[tex]P(5<x<7) = \frac{2}{8} =\frac{1}{4}[/tex]
For
[tex]x^2-12x+35 >0\\(x-5)(x-7)>0\\x<5 or x >7[/tex]
P(X<5 or x>7) = 1-P(5<x<7)
= [tex]\frac{3}{4}[/tex]
The density function of a real number selected randomly within the range [2,10] is 1/8, with the probability of an event being the difference between the two values divided by 8. The probabilities that X is greater than 5, lies between 5 and 7 and that the inequality X^2 - 12X + 35 > 0 always holds are 5/8, 1/4 and 1 respectively.
Explanation:The subject of this question is probability, particularly continuous uniform distribution. (a) A real number X selected from a certain interval [2, 10] has a continuous uniform distribution. Hence, the density function f(x) = 1/(b-a) = 1/8 for 2 ≤ x ≤ 10 and0otherwise. The probability of an event E, where E is [a,b], is the integral of f(x) from a to b, which is (b-a)/(10-2).
(b) Probability that X > 5 is the integral of f(x) from 5 to 10, which is (10-5)/8 = 5/8. Probability that 5 < X < 7 is the integral from 5 to 7, which is (7-5)/8 = 1/4. Lastly, the inequality X^2 - 12X + 35 > 0 factors out to (X-5)^2 + 10 > 0 which is always true as square number is always non-negative, thus the probability is 1.
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Find the area of the following figure: (Use π = 3.14 and do NOT include units in your answer.)
The composite shape's area is 61.12.
Step-by-step explanation:
Step 1; To calculate the value of the composite shapes area we first divide it into shapes whose areas we know. In this case, the composite shape consists of only a circle's half and a triangle attached below it. If we can sum the individual areas of the two shapes we should be able to determine the area of the unknown shape.
Step 2; The triangle has a base length of 8 as it is from (6, 10) to (14, 10) so 14 - 6 = 8 and the height is from (10,10) and (10,1) so the height is 10 -1 = 9. So the area of any given triangle is 0.5 times the product of its base length and height. So area of this triangle = 0.5 × 8 × 9 = 36. The circle is not an entire one but only half so we calculate the entire circle's area and then half it to find its area. The diameter is 8 as the circle's ends are at (6, 10) and (14, 10) and radius = 14 - 6 / 2 = 4. The area of any circle is π times the square of its radius. So area of this circle = π × r²/2= 3.14 × 4²/ 2 = 25.12.
Step 3; Now we calculate the given composite shapes area by summing the two areas i.e areas of the half-circle and the rectangle.
Area of the composite shape = 36 + 25.12 = 61.12.
A stack of nested paper cups is 8 inches tall . The 1st cup is 4 inches tall and each of the rest of the cups in the stack adds 1/4 of an inch to the height of the stack. How many cups are in the stack?
Answer:
17
Step-by-step explanation:
For n cups, the height of the stack is ...
4 + (1/4)(n -1)
For a height of 8 inches, we can find n from ...
8 = 4 +(1/4)(n -1)
4 = (1/4)(n -1) . . . . . . subtract 4
16 = n -1 . . . . . . . . . .multiply by 4
17 = n . . . . . . . . . . . .add 1
There are 17 cups in the stack.
A Television nanufacture sells 21 of TV model at$299 each, 13 of TV Model B at $549 each and 8 of TV Model C at $619 each. Find tge average price per TV Sold.
Answer:
Step-by-step explanation:
The formula for determining average is expressed as
Average = the total cost of the televisions/ the sum of the televisions
Total number of model A television that was sold is 21
Total cost of 21 televisions = 299 × 21 = $8671
Total number of model B television that was sold is 13
Total cost of 13 televisions = 549 × 13 = $7137
Total number of model C television that was sold is 6
Total cost of 6 televisions = 619 × 6 = $3714
Total number televisions sold is 21 + 13 + 6 = 40
Total cost of the televisions is 8671 + 7137 + 3714 = 19522
Therefore, the average price per TV Sold is
19522/40 = $488.05 per television
2/ 7 y+3 1/7 y if y= 7/9
Answer:
8/3 = 2 2/3
Step-by-step explanation:
(2/7)y + (3 1/7)y = (3 3/7)y = (24/7)y
For y=7/9, this is ...
(24/7)(7/9) = 24/9 = 8/3
The value of the expression for y=7/9 is 8/3.