Answer:
15(3+2x)
Step-by-step explanation:
15 multiplies to both 3 and 2x amd the result is 45+2x
Final answer:
To write an expression equivalent to 45 + 30x using the distributive property, factor out the common factor of 15 to get 15(3 + 2x).
Explanation:
To write an expression equivalent to 45 + 30x using the **distributive property**, we can factor out the common factor. This can be done as follows:
Factor out 15, so 45 + 30x becomes 15(3 + 2x).
Therefore, an expression equivalent to 45 + 30x using the distributive property is 15(3 + 2x).
a preschool has a student to teacher ratio of 5:2. The total number of students and teachers was 56 last year and is 70 this year. How many students and teachers were there for each of these two years?
Answer:
Step-by-step explanation:
student teacher ratio of 5:2....added = 7
so students make up 5/7 of the total people and teachers make up 2/7 of the total people.
Last year.....56 people
students : 5/7 * 56 = 280/7 = 40 students
teachers : 2/7 * 56 = 112/7 = 16 teachers
this year....70 total people
students : 5/7 * 70 = 350/7 = 50 students
teachers : 2/7 * 70 = 140/7 = 20 teachers
Final answer:
To find the number of students and teachers based on their ratio and total count, we applied the ratio of 5:2 to the total counts of 56 and 70 for the last year and this year, respectively. This calculation revealed there were 40 students and 16 teachers last year, and 50 students and 20 teachers this year.
Explanation:
The student has asked about finding the number of students and teachers at a preschool in two different years based on a given student-to-teacher ratio and the total count of students and teachers for those years.
Step-by-Step Solution:
First, understand the ratio of students to teachers is 5:2. This means for every 5 students, there are 2 teachers.
To solve for last year, we have a total of 56 individuals (students and teachers). Let's represent students as 5x and teachers as 2x, given their ratio. Therefore, 5x + 2x = 56, solving this gives us x = 8. This means there were 40 students (5*8) and 16 teachers (2*8) last year.
For this year, we have a total of 70 individuals. Using the same method, 5x + 2x = 70, we find that x = 10. This means there are 50 students (5*10) and 20 teachers (2*10) this year.
By understanding and applying the concept of ratios, we were able to find the number of students and teachers for both years.
Determine the following angle measures.
mZM=
mXL =
Angle measures are ∠M = 90° and ∠L = 24°
Step-by-step explanation:
Step 1: In the figure, LM is a tangent to the circle N at point M.Tangents create right angles at the point of contact with a circle.
So ∠M = 90°
Step 2: Sum of angles in a triangle is equal to 180°⇒ ∠L = 180° - (∠M + ∠N) = 180° - (90° + 66°)
= 180° - 156° = 24°
Answer:
m= 90 degrees and L= 24 degrees
Step-by-step explanation:
Please help..can't figure it out!
Answer:
B) y = x + 2 and y = -x - 4
Step-by-step explanation:
The equation of a line is represented with y = mx + b.
"x" and "y", when substituted, tell you if a point (x, y) is on the line.
"m" is slope, and tells if it goes up (positive slope) or down (negative)
"b" is the y-intercept, when the line hits the y-axis.
In the graph, we have two lines. One goes upwards (read from left to right), and the other goes downwards.
The graph that goes upwards hits the y-axis at positive "2".
The graph that goes downwards hits the y-axis at (negative) "-4".
Since the choices only have positive 1 or negative 1 as the slope, we only have to worry if it goes up or down.
Take the key information, slope and y-intercept, to write the equations.
"upwards slope, y-axis at 2"
y = x + 2
"downwards slope, y-axis at -4"
y = -x - 4
What is the reference angle for 120°? A. 30° B. 45° C. 60° D. 120° E. 240°
Answer:
C
Step-by-step explanation:
120° is an angle in the second quadrant.
The reference angle is the related acute angle in the first quadrant, that is
reference angle = 180° - 120° = 60° → C
Answer:
C
Step-by-step explanation:
A one-cup serving of orange juice Contains 4 mg less than four times the amount of vitamin C as a one cup serving of pineapple juice. Servings of two juices contain a total of 121 mg of vitamin C. How many milligrams of vitamin C are in a serving of each type of juice?
Answer:
The milligrams of vitamin C in a serving of orange juice is 96 and the milligrams of vitamin C in a serving of pineapple juice is 25
Step-by-step explanation:
Let
x ----> the milligrams of vitamin C in a serving of orange juice
y ----> the milligrams of vitamin C in a serving of pineapple juice
we know that
Servings of two juices contain a total of 121 mg of vitamin C
so
[tex]x+y=121[/tex] -----> equation A
A one-cup serving of orange juice contains 4 mg less than four times the amount of vitamin C as a one cup serving of pineapple juice
so
[tex]x=4y-4[/tex] ----> equation B
substitute equation B in equation A
[tex]4y-4+y=121[/tex]
solve for y
[tex]5y=121+4\\5y=125\\y=25\ mg[/tex]
Find the value of x
[tex]x=4(25)-4=96\ mg[/tex]
therefore
The milligrams of vitamin C in a serving of orange juice is 96 and the milligrams of vitamin C in a serving of pineapple juice is 25
A couple intends to have two children, and suppose that approximately 52% of births are male and 48% are female.
a. What is the probability both children are male?
b. What is the probability both children are female?
c. What is the probability they have exactly one male and exactly one female child?
a) Probability of both being males is 27%
b) Probability of both being females is 23%
c) Probability of having exactly one male and one female is 50%
Step-by-step explanation:
a)
The probability that the birth is a male can be written as
[tex]p(m) = 0.52[/tex] (which corresponds to 52%)
While the probability that the birth is a female can be written as
[tex]p(f) = 0.48[/tex] (which corresponds to 48%)
Here we want to calculate the probability that over 2 births, both are male. Since the two births are two independent events (the probability of the 2nd to be a male does not depend on the fact that the 1st one is a male), then the probability of both being males is given by the product of the individual probabilities:
[tex]p(mm)=p(m)\cdot p(m)[/tex]
And substituting, we find
[tex]p(mm)=0.52\cdot 0.52 = 0.27[/tex]
So, 27%.
b)
In this case, we want to find the probability that both children are female, so the probability
[tex]p(ff)[/tex]
As in the previous case, the probability of the 2nd child to be a female is independent from whether the 1st one is a male or a female: therefore, we can apply the rule for independent events, and this means that the probability that both children are females is the product of the individual probability of a child being a female:
[tex]p(ff)=p(f)\cdot p(f)[/tex]
And substituting
[tex]p(f)=0.48[/tex]
We find:
[tex]p(ff)=0.48\cdot 0.48=0.23[/tex]
Which means 23%.
c)
In this case, we want to find the probability they have exactly one male and exactly one female child. This is given by the sum of two probabilities:
- The probability that 1st child is a male and 2nd child is a female, namely [tex]p(mf)[/tex]
- The probability that 1st child is a female and 2nd child is a male, namely [tex]p(fm)[/tex]
So, this probability is
[tex]p(mf Ufm)=p(mf)+p(fm)[/tex]
We have:
[tex]p(mf)=p(m)\cdot p(f)=0.52\cdot 0.48=0.25[/tex]
[tex]p(fm)=p(f)\cdot p(m)=0.48\cdot 0.52=0.25[/tex]
Therefore, this probability is
[tex]p(mfUfm)=0.25+0.25=0.50[/tex]
So, 50%.
Learn more about probabilities:
brainly.com/question/5751004
brainly.com/question/6649771
brainly.com/question/8799684
brainly.com/question/7888686
#LearnwithBrainly
Write and equivalent expression for 5x²-15x
Answer:
x-3
Step-by-step explanation:
5x²-15x
in order to get the equivalent of the equation, simplify to the lowest term.
To simplify to the lowest term, divide through by the common factor in the equation which is 5x
5x²÷5x - 15x÷5x
=x-3
Find the equation of a line that is perpendicular to y=−12x−1 and passes through the point (3,2).
Answer:
y = (1/12)*x + 7/4
Step-by-step explanation:
y=−12x−1
Perpendicular line:
y = a*x + b
y = (1/12)*x + b
2 = (1/12) * 3 + b
2 = (3/12) + b
2 = 1/4 + b
2 - 1/4 = b
7/4 = b
Perpendicular line:
y = (1/12)*x + 7/4
How to work out the problem 491 divided by 8
Answer:
61.375
Step-by-step explanation:
Given : [tex]\frac{491}{8}[/tex]
The fraction is not dividing by a common number in numerator and denominator to simplify, So dividing the numerator directly by 8.
Gives [tex]\frac{491}{8}= 61.375[/tex]
So, 61.375 is the answer of the above problem.
What is the reciprocals of the fraction 37/74
Step-by-step explanation:
We have,
[tex]\dfrac{37}{74}[/tex]
To find, the reciprocals of the fraction [tex]\dfrac{37}{74}[/tex] = ?
∴ [tex]\dfrac{37}{74}[/tex]
Dividing numerator and denominator by 37, we get
= [tex]\dfrac{1}{2}[/tex]
= [tex]\dfrac{37}{74}[/tex] or, [tex]\dfrac{1}{2}[/tex]
We know that,
The reciprocals of the fraction [tex]\dfrac{x}{y} =\dfrac{y}{x}[/tex]
The reciprocals of the fraction [tex]\dfrac{37}{74}[/tex] = [tex]\dfrac{74}{37}[/tex] or [tex]\dfrac{2}{1}[/tex]
= [tex]\dfrac{74}{37}[/tex] or 2
Thus, the reciprocals of the fraction [tex]\dfrac{37}{74}[/tex] = [tex]\dfrac{74}{37}[/tex] or 2.
To save for a new car, Trafton invested $7,000 in a savings account that earns 6.5% interest, compounded continuously. After four years, he wants to buy a used car for $10,000. How much money will he need to pay in addition to what is in his savings account? (Round your answer to the nearest cent.)
Answer:
Trafton will need to pay $ 900 in addition to what is in his savings account, to buy the used car he wants.
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Initial deposit = $ 7,000
Annual interest = 6.5% = 0.065 compounded continuously
Time of the investment = 4 years
Price of the used car Trafton wants to buy = $ 10,000
2. How much money will he need to pay in addition to what is in his savings account?
1. For answering the question, let's calculate how much money Trafton has in his savings account after 4 years, this way:
FV = PV * e ^ (i * t)
Where,
FV = Future value of the initial deposit after t time
PV = Initial deposit
e = Euler's number (2.7183)
i = 0.065 compounded continuously
t = 4 years
Replacing with the real values, we have:
FV = 7,000 * 2.7183^(0.065 * 4)
FV = 7,000 * 1.30 (Rounding to the nearest hundredth)
FV = $ 9,100
Now, we can elaborate how much money will Trafton need to pay in addition, as follows:
Money in addition = Price of the used car Trafton wants to buy - Future Value of the savings account after 4 years
Money in addition = 10,000 - 9,100
Money in addition = $ 900
Trafton will need to pay $ 900 in addition to what is in his savings account, to buy the used car he wants.
Name a fourth point in plane TUY.
X
Y
Z
W
The answer is W, just took the test.
The graphs below have the same shape. What is the equation of the red
graph?
HELP
Answer:
The Graph below have the same shape.Equation of the red graph
Step-by-step explanation:
The graph is shifted up 1 unit. That's equivalent to adding 1 to all points:
In other words:
G(x) = F(x) + 1
Plugging in F(x) = 3 - x^4:
G(x) = 3 - x^4 + 1
G(x) = 4 - x^4
Answer:
A. G(x) = 4 - x^4
Omar has 8 cups of cornmeal how many batches of corn muffins can he make
How many cups in a batch of batter??
Answer:
16 corn muffins made.
Step-by-step explanation:
Since there is 8 cups of cornmeal, and corn muffins need 1/2 cornmeal per batch. We need to divide.
Equation: 8 divided by 1/2 = M
Then in order to divide fractions. We have to use the kcf.(Keep, change, flip)
8 is 8,(Keep) division turns into multiplication(change) and then 1/2 is 2/1 (flip).
Then multiply 8 x 2.(Since 2/1 is 2)
Your answer is 16!
Which equation best represents the line of best fit for the scatterplot?
A) y = x + 6
B) y = 2x + 6
C) y = -x + 6
D) y = -2x + 6
Answer:
The answer for this problem is
C) y = -x + 6
Step-by-step explanation:
I know this because I just did the test
The sum of two numbers is a hundred one number is at least 16 more than the other number. What are the numbers? Please help
Answer:
58 and 42.
Step-by-step explanation:
Let the 2 numbers be x and 100-x.
Also let x be the largest number, so
x ≥ 100 - x + 16 ( 'At least 16' means equal to 16 or greater than 16).
Add in x to both sides:
x + x ≥ 100 + 16
2x ≥ 116
x ≥ 58.
But since the sum of the 2 numbers is 100, x must be 58 and the other number is 42.
Pythagorus' Theroem
A rope is tied to the top of the 6m wall of a tent and tied to a peg in the ground. The peg is 2m from the bottom of the tent. How long is the rope, correct to 2d.p
A designer is making a rectangular prism box with maximum volume, with the sum of its length, width, and height 8 in. The length must be 2
times the width. What should each dimension be? Round to the nearest tenth of an inch if necessary.
Answer:
width = 1.8 in
length = 3.6 in
height =[tex]8-3w =8-3(1.8)= 2.6 in[/tex]
Step-by-step explanation:
A designer is making a rectangular prism box with maximum volume, with the sum of its length, width, and height 8 in
Let l , w and h are the length , width and height
[tex]l +w+h=8\\l=2w[/tex]
Plug it in the first equation
[tex]2w+w+h=8\\3w+h=8\\h=8-3w[/tex]
volume the box is length times width times height
[tex]volume = (2w)(w)(8-3w)\\16w^2-6w^3[/tex]
To get maximum volume we take derivatived
[tex]v'=32w-18w^2[/tex]
set the derivative =0 and solve for w
[tex]0=32w-18w^2\\0=-2w(9w-16)\\w=0 , w= \frac{16}{9}[/tex]
width = 1.8 in
length = 2w= 3.6 in
height =[tex]8-3w =8-3(1.8)= 2.6 in[/tex]
Add...- 3+(-3) =
Thank youuuu!!!!
Answer:
the answer is 0
Step-by-step explanation:
well - 3 plus 3 would just by 0 because if the number with the negative is the biggest then the answer is negative but if the positive number is the biggest then the answer would be positive because there is not a bigger number it would be 0 because 3 and -3 have pretty much the same value other then them being negative and positive
The distance from the equator to the north pole is almost 10,000 km. Roughly how many kilometers is: the distance around the earth at the equator? 1 degree of longitude?
Step-by-step explanation:
As the distance from the equator to the north pole is almost 10,000 km.
The reason is that the definition of a meter is [tex]1\:10,000,000th[/tex] of the distance from the North Pole to the equator. Thus, itʹs exactly [tex]10,000,000[/tex] meters from the North Pole to the equator, that is exactly 10,000 kmAs we know that
An equator is basically termed as an imaginary line around the middle of a planet - midway between the South and the North Pole, at [tex]0[/tex] degrees latitude.An equator cuts the planet into a Southern and a Northern HemisphereAs the planet Earth is outspread or widest at its Equator and the distance around the Earth at the Equator - its circumference - is [tex]24,901\:miles[/tex].
[tex]24,901\:miles\:=\:40,075\:kilometers[/tex]
So, the distance around the Earth at the Equator - its circumference - is [tex]40,075\:kilometers[/tex].
Also, at the equator, [tex]1^{0}[/tex] ( [tex]1\:degree[/tex] ) of longitude and latitude both cover about [tex]111[/tex] km, or just under [tex]70[/tex] miles.
Keywords: equator, longitude, north pole
Learn more about longitude and north pole from brainly.com/question/13281490
#learnwithBrainly
A bank offers 2.12 interest compounded annually for investing money in a savings account, you open an account with $300. How much money in interest big you leave it for 10 years
Answer:
[tex]\large \boxed{\$70.02}[/tex]
Step-by-step explanation:
The compound interest formula is
[tex]A = P\left(1 + \dfrac{r}{n}\right)^{nt}[/tex]
Data:
P = 300
r = 2.12 % = 0.0212
t = 10 yr
n = 1 calculation per year
1. Accrued amount:
A = 300(1+ 0.0212)¹⁰
= 300 × 1.0212¹⁰
= 300 × 1.233 41
= 370.02
2. Interest
I = A - P = 370.02 - 300.00 = 70.02
[tex]\text{The interest is $\large \boxed{\mathbf{\$70.02}}$}[/tex]
Final answer:
Using the compound interest formula, investing $300 at an annual interest rate of 2.12% compounded annually for 10 years will result in approximately $70.37 in interest, totaling $370.37.
Explanation:
A bank offers 2.12% interest compounded annually for investing money in a savings account, and you open an account with $300. How much money in interest will you earn if you leave it for 10 years?
To calculate the amount of money you will have after 10 years, including interest, you can use the formula for compound interest: [tex]A = P(1 + r/n)^{(nt)[/tex], where:
P = principal amount (initial investment) is $300,r = annual interest rate in decimal form, which is 0.0212 for 2.12%,n = number of times the interest is compounded per year, which is 1 since it's compounded annually,t = time the money is invested for in years, which is 10 years.Plugging these values into the formula gives us: [tex]A = $300(1 + 0.0212/1)^{(1*10)[/tex] = [tex]$300(1 + 0.0212)^{10[/tex] = [tex]$300(1.0212)^{10.[/tex]
Calculating this, we get A = $300(1.234567), which equals approximately $370.37. Therefore, the total interest earned over 10 years is approximately $70.37.
ASAP PLEASE ANSWER THIS WILL GIVE BRAINLIEST
The rectangle shown has a perimeter of 86 cm and the given area. Its length is 7 more than three times its width. Write and solve a system of equations to find the dimensions of the rectangle.

A= 306cm squared
A is the rectangle
Answer:
Therefore,
The Dimensions are,
[tex]Length = 34\ cm\\\\Width = 9\ cm[/tex]
Step-by-step explanation:
Given:
Perimeter of a rectangle,
Perimeter = 86 cm
let "x" be the width of rectangle,
Width = x
then according to the given condition,
length will be given as,
[tex]Length = 3x+7[/tex]
To Find:
Length =?
Width =?
Solution:
Perimeter of rectangle is given by,
[tex]\textrm{Perimeter of Rectangle}=2(Length+Width)[/tex]
Substituting the values we get
[tex]86=2(3x+7+x)\\\\86=2(4x+7).........Equation\\\\86=8x+14\\\\8x=86-14=72\\\\x=\dfrac{72}{8}=9\ cm[/tex]
Substituting "x" in Length we get
[tex]Length = 3\times 9 +7=34[/tex]
Also Area Of Rectangle is given by
[tex]\textrm{Areaof Rectangle}=(Length\times Width)=34\times 9=306\ cm^{2}[/tex]
Therefore,
The Dimensions are,
[tex]Length = 34\ cm\\\\Width = 9\ cm[/tex]
Final answer:
The dimensions of the rectangle with an area of 306 cm squared and a perimeter of 86 cm, where the length is 7 more than three times the width, are 9 cm by 34 cm.
Explanation:
To solve for the dimensions of the rectangle with an area of 306 cm squared and a perimeter of 86 cm, where the length (L) is 7 more than three times the width (W), we will set up a system of equations. First, express the given relationships:
Perimeter (P) = 2W + 2L = 86 cm
Area (A) = W * L = 306 cm squared
L = 3W + 7
Next, substitute the expression for L into the perimeter equation:
2W + 2(3W + 7) = 86
2W + 6W + 14 = 86
8W + 14 = 86
8W = 72
W = 9 cm
Now, plug the value of W back into the equation for L:
L = 3(9) + 7 = 34 cm
Thus, the dimensions of the rectangle are 9 cm by 34 cm.
Solve the following expression. 36 - {-49 + (32.9) ] =
Answer:
52.1
Step-by-step explanation:
The given expression is 36 - [-49 + 32.9]
First we have to simplify the numbers which are in parenthesis.
= 36 -(-16.1)
Here -(-16.1) = + 16.1
So, we get
= 36 + 16.1
= 52.1
The answer is 52.1
Manny runs 15 3/4 miles each week. Zander runs 5/6 as many miles each week as Manny.
How many miles does Zander run each week?
In these kinds of problems, take 15 and 3/4 (Manny's distance) and multiply it by the factor 5/6. (15 3/4 = 15.75)
(15.75) * (5/6) = 13.125 = 13 1/8
This should get you 13 and 1/8 miles for Zander's distance.
The Pet-Agree Co. buys dog collars from a manufacturer for $1.19 each. Pet-Agree marks-up each collar 356% of cost. What is the amount of mark-up?
The amount of mark-up is $4.25
Step-by-step explanation:
To find the mark-up cost of each dog collar, increase $1.19 by 356 %
Lets take that 100% = $1.19
So the 356% =?
Perform cross-product as;
(356*1.19)/100 = $4.25
Learn More
Percent increase : https://brainly.com/question/11537235
Keywords : Dog collars, manufacturer, mark-up, cost , amount
#LearnwithBrainly
Answer:
4.25
Step-by-step explanation:
I did the quiz
Order the absolute values of the temperatures from least to greatest. -22, -6, 15, -13, 18
Answer:
6 13 15 18 22
Step-by-step explanation:
absolute value just makes it positive unless it is a negative absolute value-|n|
A glass of cold water is removed from a refrigerator whose interior temperature is 39°F into a room maintained at 72°F. One minute later the temperature of the water is 43°F. What is the temperature of the water after 9 minutes? (Round your answers to two decimal places.)
°F
What is the temperature of the water after 28 minutes?
°F
Choose the missing exponent to create a polynomial: 3x^4+4x^2-9x^-?+2
?=Missing Value
A) 2
B) 3
C) -9
D) 7
E) 4
Answer:
C) -9
Step-by-step explanation:
Exponents in a polynomial must be positive integers. Since your ? has a minus sign in front, its value must be negative. The only such choice is C.
What is the surface area of this triangular prism rounded to the nearest tenth?
A) 133.5 ft2
B) 145.3 ft2
C) 152.6 ft2
D) 163.7 ft2
Answer:
The surface area of the triangular prism is [tex]145.3[/tex] [tex]ft^2[/tex]
Step-by-step explanation:
Step 1: Finding the two area of two triangles
Area of the triangle = [tex]\frac{1}{2} (base \times height})[/tex]
Area of the triangle = [tex]\frac{1}{2} (9.8\times 5.33})[/tex]
Area of the triangle = 26.117
Area of 2 triangles = [tex]52.234[/tex]
Step 2: Finding the area of the side rectangles
Area of the rectangle = [tex]length \times breadth[/tex]
Area of the rectangle 1 = [tex]6.2 \times 3.8[/tex] = 23.56 [tex]ft^2[/tex]
Area of the rectangle 2 = [tex]8.5 \times 3.8[/tex] = 32.3 [tex]ft^2[/tex]
Area of the rectangle 3 = [tex]9.8 \times 3.8[/tex] = 37.24 [tex]ft^2[/tex]
Step 3: surface area of the triangular prism.
Surface area of the triangular prism = 52.234 + 23.56 + 32.3 + 37.24
Surface area of the triangular prism = 145.334 [tex]ft^2[/tex]
Answer:
B. 145.3 ft2
Step-by-step explanations:
Suppose a small airplane has a wingspan of 15 feet. Find the wingspan of a model of the airplane, in inches, if the scale factor is 1/60.
A) 3 inches
B) 4 inches
C) 6 inches
D) 12 inches
Answer: 3 inches
Step-by-step explanation:
1/60 = x/15,
x = 1/4
1/4 foot = 3 inches.