Final answer:
The customer would need to have 25 small gifts to wrap in order for the costs to be the same, whether using the department store's service at $2 per gift or paying his niece the $50 flat fee.
Explanation:
To determine how many small gifts need to be wrapped to make the cost the same whether paying his niece the flat fee of $50 or paying the department store $2 per gift, we can set up a simple equation:
Let x represent the number of small gifts.
Then, the cost of wrapping at the department store is $2 per gift, which means the cost is 2x dollars.
The niece's flat fee is $50, regardless of the number of gifts.
The equation to find the breakeven point where both options cost the same is:
2x = 50
Solving for x gives us:
x = 50 / 2
x = 25 gifts
Thus, if the customer has 25 small gifts to wrap, it would cost the same to have them wrapped by his niece at a flat rate or by the department store per gift.
A line intersects the points (14, -3) and (9, -11).
Find the slope of the line and simplify completely.
Slope =
Answer:
8/5 or 1 3/5
Step-by-step explanation:
What's 10 percent of 80
Answer:
8
Step-by-step explanation:
[tex]\frac{is}{of} = \frac{percent}{100}[/tex]
[tex]\frac{x}{80} = \frac{10}{100}[/tex]
80x10 = 800
800 = 100x
800 divide 100 = 8
answer = 8
Hope this helped!! :)
40 points please help
Problem:
The altitude of an airplane descending to the airport is represented by the equation shown below, where y represents the altitude, in feet, of the airplane and x, represents the number of minutes after descending.
y = -500x + 28,000
Part A:
What is the altitude of the airplane after 5 minutes? after 30 minutes? Show your work then write your answers as ordered pairs (x,y).
Part B:
Create a table for the values when x = 0, 5, 8, 10, 30.
Part C:
Which ordered pair (from the table in part B) represents the initial value? What does the initial value represent in this problem? (1-2 sentences)
Part D:
What is the rate of change in this equation? What does the rate of change represent in this problem? (1-2 sentences)
answer:
im not sure. what is ur question
step-by-step explanation:
Hector Drew three rectangles to show the letter H on his notebook use the rectangles to find the area of the letter he drew
Answer:
Step-by-step explanation:
The area of the H is 86
Answer: Just draw a line at the end of each
Step-by-step explanation: Like this
H I I at the end
Gumballs are 2 for 8 cents. How many gumballs can I buy for 32 cents?
Answer:
8 gumballs.
Step-by-step explanation:
How many cents you have divided by the cost:
32 divided by 8 = 4
The answer times the amount of gumballs:
4 x 2 = 8
8 gumballs.
Solve. 5a−12=−2 plzz help
Answer:
a=2
Step-by-step explanation:
Given: 5a-12=-2
Isolate Variable: 5a=10
Divide: a=2
Answer:
5a - 12= -2
5 x 2= 10 so,
5(2) - 12= -2
^
10-12= -2
Which set of numbers could represent the lengths of the sides of a right triangle?
8, 15, 17
10, 15, 20
12, 18, 22
7,9, 11
Answer:
The first set: 8, 15, and 17.
Step-by-step explanation:
Pair: 8, 15, 17By the pythagorean theorem, a triangle is a right triangle if and only if
[tex]\text{longest side}^2 = \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
In this case,
[tex]\text{longest side}^2 = 17^2 = 289[/tex].
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 8^2 + 15^2\\ &=64 + 225 = 289 \end{aligned}[/tex].
In other words, indeed [tex]\text{hypotenuse}^2 = \text{first leg}^2 + \text{second leg}^2[/tex]. Hence, 8, 15, 17 does form a right triangle.
Similarly, check the other pairs. Keep in mind that the square of the longest side should be equal to the sum of the square of the two
Pair: 10, 15, 20Factor out the common factor [tex]2[/tex] to simplify the calculations.
[tex]\text{longest side}^2 = 20^2 = 400[/tex]
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 10^2 + 15^2\\ &=100 + 225 = 325 \end{aligned}[/tex].
[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
Hence, by the pythagorean theorem, these three sides don't form a right triangle.
Pair: 12, 18, 22[tex]\text{longest side}^2 = (2\times 11)^2 = 2^2 \times 121[/tex].
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= (2 \times 6)^2 + (2 \times 9)^2\\ &=2^2 \times(36 + 81) = 2^2 \times 117 \end{aligned}[/tex].
[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
Hence, by the pythagorean theorem, these three sides don't form a right triangle.
Pair: 7, 9, 11[tex]\text{longest side}^2 = 11^2 = 121[/tex].
[tex]\begin{aligned}&\text{first shortest side}^2 + \text{second shortest side}^2 \\ &= 7^2 + 9^2\\ &=49+ 81 = 130 \end{aligned}[/tex].[tex]\text{longest side}^2 \ne \text{first shorter side}^2 + \text{second shorter side}^2[/tex].
Hence, by the pythagorean theorem, these three sides don't form a right triangle.
3x − 14y = –20 what the answer i need help please
Answer:
Boooommm x= -2
Step-by-step explanation:
3x − 14y = –20
ok so 3x-14y=-20
+14 to invert the fraction
-20+14=-6
3x=-6
-6/3=-2
x=-2
Find the number of terms of this polynomial. 5x^2 + 3x - 4 (2 point)
Number of terms:
There are three terms in polynomial
Solution:
Given polynomial is:
[tex]5x^2+3x-4[/tex]
We have to find the number of terms in polynomial
A term can be a signed number, a variable, or a constant multiplied by a variable or variables
When a term is made up of a constant multiplied by a variable or variables, that constant is called a coefficient.
Therefore, terms in polynomial are:
[tex]5x^2+3x-4\\\\Terms: 5x^2 \text{ and 3x and -4 }[/tex]
Thus there are three terms in polynomial
The lifespans of tigers in a particular zoo are normally distributed. The average tiger lives 22.4 years; the
standard deviation is 2.7 years.
Use the empirical rule (68 - 95 - 99.7%) to estimate the probability of a tiger living between 27.8 and 30.5
years.
Answer:
[tex] P(27.8 < X <30.5)=P(X>27.8)-P(X>30.5)=0.025-0.0015=0.0235[/tex]
Step-by-step explanation:
The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ)".
Let X the random variable who represent the lifespans of tigers in a particular zoo.
From the problem we have the mean and the standard deviation for the random variable X. [tex]\mu=120 , \sigma=110[/tex]
On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:
• The probability of obtain values within one deviation from the mean is 0.68
• The probability of obtain values within two deviation's from the mean is 0.95
• The probability of obtain values within three deviation's from the mean is 0.997
We want to find this probability:
[tex] P(27.8 < X <30.5)[/tex]
And in order to calculate how many deviation we are above/below the mean we can use the z score given by:
[tex]z =\frac{x-\mu}{\sigma}[/tex]
And if we use this formula for the two values given we have:
[tex] z_1 = \frac{27.8-22.4}{2.7}=2[/tex]
[tex] z_1 = \frac{30.5-22.4}{2.7}=3[/tex]
So we have values between 2 and 3 deviations above the mean.
We can use the following probabilities
[tex]P(X<\mu -\sigma)=P(X <19.7)=0.16[/tex]
[tex]P(X>\mu +\sigma)=P(X >25.1)=0.16[/tex]
[tex]P(X<\mu -2*\sigma)=P(X<17)=0.025[/tex]
[tex]P(X>\mu +2*\sigma)=P(X>27.8)=0.025[/tex]
[tex]P(X<\mu -3*\sigma)=P(X<14.3)=0.0015[/tex]
[tex]P(X>\mu +3*\sigma)=P(X>30.5)=0.0015[/tex]
And we can find this probability on this way:
[tex] P(27.8 < X <30.5)=P(X>27.8)-P(X>30.5)=0.025-0.0015=0.0235[/tex]
To estimate the probability of a tiger's lifespan falling between 27.8 and 30.5 years, we can use the empirical rule, which states that approximately 95% of the data falls within two standard deviations of the mean.
Explanation:To estimate the probability of a tiger living between 27.8 and 30.5 years, we can use the empirical rule. According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean, and approximately 95% falls within two standard deviations. Since the mean is 22.4 years and the standard deviation is 2.7 years, we need to find the probability that a tiger's lifespan falls between 27.8 - 22.4 = 5.4 years and 30.5 - 22.4 = 8.1 years.
Since 5.4 years and 8.1 years are less than two and three standard deviations away from the mean, respectively, the probability can be estimated to be approximately 95% using the empirical rule.
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pls, help!!!!!!!!!!!!!!!!!!!!! I need help with the problem. I'm stuck!!!!! Write an inequality from this sentence. Kevin sells at most $60 worth of drinks in the concession stand.
Answer:
i) let x be the amount of money worth of drinks that Kevin sold.
ii) Kevin sells at most $60 worth of drinks.
iii) therefore the inequality can be written as
x ≤ $60
Step-by-step explanation:
i) let x be the amount of money worth of drinks that Kevin sold.
ii) Kevin sells at most $60 worth of drinks.
iii) therefore the inequality can be written as
x ≤ $60
3. The Assistant Principal for Curriculum administered a practice SAT test with 50 questions
to students during an after-school tutoring program. She said a score of 30 or above predicts
a good SAT test score. How many students took the test and how many can expect a good
SAT test score?
O
O
A. 28 students took the test and 14 of them can expect a good SAT test score.
B.28 students took the test and 4 of them can expect a good SAT test score.
C. 28 students took the test and 21 of them can expect a good SAT test score.
D. 26 students took the test and 14 of them can expect a good SAT test score.
OO
O Mark for review (Will be highlighted on the review page)
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Answer:
A
Step-by-step explanation:
Answer:
the answer is c
Step-by-step explanation:
By what number would you multiply 9/5 to get a product of -1
You should multiply [tex]\frac{9}{5}[/tex] with [tex]\frac{-5}{9}[/tex] to get a product of -1
Solution:
Let the number to be multiplied be "a"
Given that,
By what number would you multiply 9/5 to get a product of -1
'a" multiplied with 9/5 should give a product -1
Therefore, writing it mathematically we get,
[tex]a \times \frac{9}{5} = -1[/tex]
Solve the above equation for "a"
[tex]a \times \frac{9}{5} = -1\\\\a = -1 \times \frac{5}{9}\\\\a = \frac{-5}{9}[/tex]
Therefore, you should multiply [tex]\frac{9}{5}[/tex] with [tex]\frac{-5}{9}[/tex] to get a product of -1
Final answer:
To multiply 9/5 by a number to get -1, you must multiply it by -5/9. This is found by setting up an equation to solve for the unknown number and then isolating the variable on one side of the equation.
Explanation:
To find by what number you would multiply 9/5 to get a product of -1, we can set up an equation that represents this situation:
Let x be the number we are looking for. Then we have the equation: (9/5) × x = -1
To solve for x, we need to divide both sides of the equation by (9/5): x = -1 ÷ (9/5)
Multiplying by the reciprocal of (9/5), which is (5/9), we get:
x = -1 × (5/9)
x = -5/9
Therefore, you must multiply 9/5 by -5/9 to get a product of -1.
What is –36° converted to radians?
Negative 5 pi
Negative StartFraction 5 Over pi EndFraction
Negative StartFraction pi Over 5 EndFraction
Negative one-fifth
Option c: [tex]-\frac{\pi}{5}[/tex] is the correct answer.
Explanation:
The given degree is –36°
Since, [tex]1^{\circ}=\frac{\pi}{180}[/tex]
The radian of –36° can be determined by multiplying it with [tex]\frac{\pi}{180}[/tex]
Thus, the degree can be converted into radians, by multiplying the degree with [tex]\frac{\pi}{180}[/tex]
Hence, it can be written as
[tex]-36^{\circ} \times \frac{\pi}{180}[/tex]
Multiplying, we get,
[tex]\frac{-36^{\circ} \pi}{180}[/tex]
Dividing, we have,
[tex]-\frac{\pi}{5}[/tex]
Thus, the radian of -36° is [tex]-\frac{\pi}{5}[/tex]
Answer:
the answer is c
Step-by-step explanation:
In the morning, sophie goes to the store the goes to school. In the afternoon she goes from school to her house. The map shows the distance between school and home as 5 cm. If every 4 cm on the scale drawing equals 8 kilometers, how far apart are sophies home and school.
10 km
Step-by-step explanation:
If 4 cm represents 8 kilometers then 1 cm represents;
8 / 4
= 2
1 cm : 2 km
How, then, about 5 cm – the distance between Sophie's home and school?
5 cm : ? km
A cross multiplication;
1 cm : 2 km
5 cm : x km
(5 * 2) = 1 x
x = 10/1
x = 10
Function 1: y = 4x + 5 Function 2: The line passing through the points (1, 6) and (3, 10). Which of these functions has the greater rate of change? A) Function 1, because the slope is 5 and the slope of function 2 is 4. B) Function 1, because the slope is 4 and the slope of function 2 is 2. C) Function 2, because the slope is 7 and the slope of function 1 is 5. D) Function 2, because the slope is 5 and the slope of function 1 is 4. Eliminat
Answer:
Step-by-step explanation:
function 1 : y = 4x + 5
In y = mx + b form, which is what ur equation is in, the slope can be found in the m position. So the slope of this function is 4.
function 2 : (1,6),(3,10)
slope = (y2 - y1) / (x2 - x1)
(1,6)...x1 = 1 and y1 = 6
(3,10)...x2 = 3 and y2 = 10
now we sub
slope = (10 - 6) / (3 - 1) = 4/2 = 2
B. Function 1, because the slope is 4 and the slope of function 2 is 2. <==
Answer:
Function 1, because the slope is 4 and the slope of function 2 is 2. Use the slope formula.
you earned 139.20 in simple interest off of 1450 investment in 8 years. What is your annual percentage rate?(Expressed as a percent)
The annual percentage rate is: 1.2%
Step-by-step explanation:
The formula for calculating simple interest is:
[tex]I = Prt[/tex]
Here
P is the principal amount
r is the interest rate
t is the time in years
We are Given:
[tex]P = 1450\\t = 8\ years\\I = 139.20[/tex]
Putting the values in the formula
[tex]139.20 = 1450 * r * 8\\139.20 = 11600r[/tex]
Dividing both sides by 11600
[tex]\frac{11600r}{11600} = \frac{139.20}{11600}\\r = 0.012[/tex]
Converting into percentage
r = 0.012*100
r = 1.2%
Hence,
The annual percentage rate is: 1.2%
Keywords: Percentage, interest
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start time 7:30am elapsed time 2hour,20 minutes end time
Answer:
End time = 9:50
Step-by-step explanation:
Elapsed time = End time - start time
End time = Elapsed time + start time
End time = 2 hour,20 minutes + 7:30
End time = 9:50
A bag of turf builder sun and shade mix grass seed covers an area of 4000ft.How many bags are needed to cover an area of 35,000ft
Answer: you will get 8.75, but the answer should be 9 bags
Step-by-step explanation:
Write an equation that represents "eight more than twice a number is fifty".
Answer:
8+2x=50
happy to help!!
You start out with $20 and then spend money in a store where every item is $3. Y = -3x + 20.
D
Step-by-step explanation:
find the equation of the line shown
Answer:
[tex]y = 2x - 1[/tex]
Step-by-step explanation:
The line shown is a straight line its equation is of the form.
[tex]y = mx + c[/tex]
Where m is the slope and c is the y-intercept.
From the graph, the slope is
[tex]m = \frac{rise}{run} [/tex]
[tex]m = \frac{2}{1} = 2[/tex]
The y-intercept from the graph is where the line intersects the y-axis, so c=-1
We substitute the values to get:
[tex]y = 2x - 1[/tex]
Explanation of how to find the equation of lines based on their slopes and intercepts.
Explanation:Equation of the line: The equation of the left line is y = -x + 1 and the equation of the right line is y = 1/2x - 1/2.
Using Slope-Intercept Form: The slope-intercept form of the equation y = mx + b helps determine the equations of lines based on their slopes and intercepts.
Point-Slope Formula: By using the point-slope formula, which utilizes a point on the line and the line's slope, we can find the equation of a line.
dividing fractions
21/32 ÷ 3/5
Answer:
105/96
Step-by-step explanation:
Answer:
In dividing fractions, you do the inverse. (Also called the reciprocal.)
So take that attachment you attached as a example.
21 3 21 5
---- ÷ ---- = ------ ÷ ------
32 5 32 3
Another reminder, when you find the reciprocal, you now multiply instead of divide. (Do not question the math world. I questioned it, and I paid the price. TnT)
So 21/32 multiplied by 5/3 would be....
21 5 105
----- × ----- = -------
32 3 96
You could leave it that way, or simplify it.
Simplest form is-
1 3/32
Non-simplified form is-
105/96
Good night and have a good day~
(Well at least, I'm going to sleep)
What is the value of x?
Enter your answer in the box.
Answer:
Since the two angles are across from each other that tells us that they are equal in length, so we want to set them equal to each other
3x+50=6x-10, Now we want to solve it like a normal equation, get x by itself
First add 10 to each side
3x+50+10=6x-10+10
3x+60=6x
Now we want to subtract 3x from each side
3x-3x+60=6x-3x
60=3x
Now divide both sides by 3
60/3=3x/3
20=x
x=20
Hope this helps ;)
Step-by-step explanation:
Please help
Find the volume for each individual shape
Find the composite volume of the original figure.
Answer:
92.11 cm³
Step-by-step explanation:
The figure below;
Has two hemispheres, and An open cylinder The radius of the hemisphere is 2 mmThe height of the cylinder is 6 mm (10 mm - 4 mm)We are required to determine the volume of the figure;
The volume of a hemisphere is given by;
Volume hemisphere = 2/3πr³
Taking π to be 3.14
The Volume of the two hemisphere;
= 2/3 × 3.14 × 2³
= 16.75 cm³
Volume of the cylinder;
Volume = πr²h
= 3.14 × 2² × 6
= 75.36 cm³
Thus, volume of the figure;
= 16.75 cm³ + 75.36 cm³
= 92.11 cm³
Hence, the volume of the figure is 92.11 cm³
simplify this,(p-5)^2-49
Answer:
(p - 12)(p + 2) or
p^2 - 10p - 24.
Step-by-step explanation:
We use the Difference of 2 Squares Identity.
a^2 - b^2 = (a - b)(a + b).
So (p - 5)^2 - 49
= (p - 5 - 7)(p - 5 + 7)
= (p - 12)(p + 2)
= p^2 - 10p - 24.
Answer:
(p - 12)(p + 2)
Step-by-step explanation:
(p-5)² - 49 =
= (p - 5 - 7)(p - 5 + 7)
= (p - 12)(p + 2)
a² - b² = (a - b)(a + b)
a = p - 5
b = 49
What is the area Of a circle that has a circumference of 10 pi.
Answer:
circumference = 10 pi = 2r pi
then r =5
next area of circle = 5 .5.pi = 25 pi
Step-by-step explanation:
The value of the expression when n=2 is
Answer:
2/3
Step-by-step explanation:
(3 tablespoons of butter; 38 Jet-Puffed Marshmallows; and 6 cup of kellogg's rice krispies cereal) yields 12 servings. Janice is an expert at making these treats. For the upcoming Christmas Party, she is expecting 30 people & would like for EVERYONE to get 4 servings EACH. How many of each ingredient will she need?
Answer:
Janice required 30 tablespoons of butter, 380 Jet-Puffed Marshmallows and 60 cup of Kellogg's rice krispies cereal to yield 120 servings.
Step-by-step explanation:
Given that 3 tablespoons of butter, 38 Jet-Puffed Marshmallows, and 6 cup of Kellogg's rice krispies cereal) yields 12 servings.
Now, Janice has to make for 30 people and each with 4 servings for the Christmas Party.
So, there are total (30 × 4) = 120 servings required to make.
So, each and every ingredients of the dish will be required to be made 10 times.
Therefore, Janice required 30 tablespoons of butter, 380 Jet-Puffed Marshmallows and 60 cup of Kellogg's rice krispies cereal to yield 120 servings. (Answer)
Janice will need 30 tablespoons of butter, 380 marshmallows, and 60 cups of rice krispies cereal for the Christmas Party.
Explanation:To find out how many of each ingredient Janice will need, we need to calculate the total servings required for the Christmas Party. She is expecting 30 people and wants everyone to have 4 servings each. So the total servings required would be 30 * 4 = 120 servings.
Now, we can calculate the ratio of servings to each ingredient. If 12 servings require 3 tablespoons of butter, then 120 servings would require (120/12) * 3 = 30 tablespoons of butter.
Similarly, if 12 servings require 38 marshmallows, then 120 servings would require (120/12) * 38 = 380 marshmallows. And if 12 servings require 6 cups of rice krispies cereal, then 120 servings would require (120/12) * 6 = 60 cups of rice krispies cereal.
So, Janice will need 30 tablespoons of butter, 380 marshmallows, and 60 cups of rice krispies cereal for the Christmas Party.
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What is
p² + (p +7)²=169
Answer:
-12 or 5
Step-by-step explanation:
p² + (p+7)² = 169
p² + (p²+14p+49) = 169
2p² + 14p + 49 - 169 = 0
2p² + 14p - 120 = 0
2p² + 24p - 10p - 120 = 0
2p(p+12) - 10(p+12) = 0
(p+12)(2p-10) = 0
p+12 = 0 , or 2p-10 = 0
p = -12 or 5
Answer:
p = 3
Step-by-step explanation:
p² + (p +7)²=169
Open the bracket and solve the value in the bracket according to BODMAS
p^2 + p^2 + 7^2 = 13^2
Square Root the both side of the equation.
√{p^2} + √{p^2} + √{7^2} = √{13^2}
p + p +7 = 13
2p + 7 = 13
collect like term of the numbers
2p = 13 - 7
2p = 6
Divide both side by the coefficient of p.
2p/2 = 6/2
p = 3.