Answer:
12
Step-by-step explanation:
f(x)=3x+9
f(12) = 3*12 +9
36+9
45
f(8) = 3*8+9
=24+9
= 33
f(12) - f(8) = 45-33
12
A bank offer 3% interest each yr you invest 1500. Write a equation to model this situation for x years. How much will be in the account after 10 years?
Answer:
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = 1500
r = 3% = /100 = 0.0
n = 1 because it was compounded once in a year.
t = x years
Therefore, the equation to model this situation is
A = 1500(1 + 0.03/1)^1 × x
A = 1500(1.03)^x
When x = 10 years, then
A = 1500(1.03)^10
A = $2016
Three bags of dog food cost $26.88, including tax. Jerry has $50.00. How many bags of dog food can Jerry buy?
Answer:
1 bag
Step-by-step explanation:
Jerry only has $50.00 if 1 bag costs $26.88, even without taxes, he can only buy 1 bag because 26.88+26.88=53.76
Twenty college students experience the effects of alcohol on reaction time. They perform very basic timed responses in a driving simulator both before and after consuming several alcoholic beverages. The researcher collects a reaction-time result for each of the 20 students before and after intoxication, for a total of 40 measures. What is the null hypothesis for this paired-samples study?
Answer:
For this case the hypothesis would be that after consuming alcoholic beverages the reaction time increases, so then the system of hypothesis for this case are:
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x \leq 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x >0[/tex]
We can define the difference as: [tex]d_i=y_i-x_i[/tex]
And the system of hypothesis are:
Null hypothesis:[tex] \mu_d \leq 0[/tex]
Alternative hypothesis: [tex] \mu_d >0[/tex]
Step-by-step explanation:
Previous concepts
A paired t-test is used to compare two population means where you have two samples in which observations in one sample can be paired with observations in the other sample. For example if we have Before-and-after observations (This problem) we can use it.
Let put some notation
x=test value before , y = test value after
Solution to the problem
For this case the hypothesis would be that after consuming alcoholic beverages the reaction time increases, so then the system of hypothesis for this case are:
The system of hypothesis for this case are:
Null hypothesis: [tex]\mu_y- \mu_x \leq 0[/tex]
Alternative hypothesis: [tex]\mu_y -\mu_x >0[/tex]
We can define the difference as: [tex]d_i=y_i-x_i[/tex]
And the system of hypothesis are:
Null hypothesis:[tex] \mu_d \leq 0[/tex]
Alternative hypothesis: [tex] \mu_d >0[/tex]
What is the slope of the line shown
Answer: The Option is A, slope is -1/3
Step-by-step explanation:
Divide 45 in the ratio 7:8
Answer:
0.0195?
Step-by-step explanation:
Answer:
21 : 24
Step-by-step explanation:
Sum the parts of the ratio, 7 + 8 = 15 parts
divide 45 by 15 to find one part of the ratio
45 ÷ 15 = 3 ← value of 1 part of ratio, thus
7 parts = 7 × 3 = 21
8 parts = 8 × 3 = 24
45 divided in the ratio 7 : 8 is 21 : 24
Robert delivers papers every morning. On Sundays he has to deliver 57 papers and on each of the other days he only has to deliver 36 papers. How many papers does Robert deliver each week?
A.
309
B.
399
C.
345
D.
273
Reset Submit
Answer:
D. 273
Step-by-step explanation:
(36*6)+57
216+57
273
Talulah is an ecologist who studies the change in the penguin population of Antarctica over time. She observed that the population decays by a factor of 8/9 every 4 months. The population of penguins can be modeled by a function, P, which depends on the amount of time, t (in months). When Talulah began the study, she observed that there were 27,000 penguins in Antarctica. Write a function that models the population of the penguins t months since the beginning of Talulah's study. P(t) =
Answer:
P(t) = 27000 * (8/9)^(t/4)
Step-by-step explanation:
The population of penguins in Antarctica decays by 8/9 every 4 months, starting from an initial count of 27,000. The function for the penguin population P(t) after t months is P(t) = 27,000 × (8/9)^(t/4).
Explanation:Talulah, an ecologist, has observed that the population of penguins in Antarctica decays by a factor of 8/9 every 4 months. To model this decay, we can use an exponential decay function. Given that the initial population (P0) is 27,000 penguins, the function P(t) that models the population at time t (in months) since the beginning of Talulah's study is:
P(t) = P0 × (decay factor)(t/rate period)
Where P0 is the initial population, the decay factor is 8/9, and the rate period is 4 months. Plugging in these values gives us:
P(t) = 27,000 × (8/9)(t/4)
This function allows researchers to predict the penguin population at any given time t months after Talulah's initial observation.
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which cannot be a cross section of the figure? A cross section of the figure cannot be a ____
Answer:
it is circle
Step-by-step explanation:
just got it correct
Ryan is building a ramp so he can easily move things in and out of an overhead storage area in his garage. The storage area is 8 feet off the ground, and Ryan has 15 feet of space along the ground to build the ramp.
A triangle with side lengths 15 feet, 8 feet, and an unlabeled hypotenuse.
What is the length of the ramp Ryan will build?
7 feet
10 feet
17 feet
23 feet
Answer:
17 feet
Step-by-step explanation:
c=the length of the ramp
a=8 ft
b=15 ft
Pythagorean Theorem
c²=a²+b²
c²=8²+15²
c²=64+225
c²=289
c=√289
c=17 ft
The length of the ramp of the triangular path is AC = 17 feet
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the base of the ramp is BC = 15 feet
The height of the ramp is AB = 8 feet
So , length of the ramp Ryan needs to build is AC is
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
AC = √ ( AB )² + ( BC )²
AC = √ ( 8 )² + ( 15 )²
AC = √ ( 64 + 225 )
AC = √289
AC = 17 feet
Therefore , the value of AC is 17 feet
Hence , the length of the ramp is 17 feet
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The combination of Wendell and Maggie’s ages is 33. Wendell’s age is 3 less than 3 times the age of Maggie. How old is Wendell?
Answer:
Wendell is 24 years old.
Step-by-step explanation:
First write an equation to represent the situation.
x=Maggie's age
x+(3x-3)=33
Then solve for x
x+3x-3=33
4x-3=33
4x-3+3=33+3
4x=36
4x/4=36/4
x=9
Then solve for Wendell's age
y=Wendell's age
y=3x-3
y=3(9)-3
y=27-3
y=24
Wendell is 24 years old.
By setting up and solving a system of equations based on the information given, we find that Wendell is 24 years old.
Explanation:In this question, we are asked to find out Wendell's age. First, we assume that Maggie's age is x. According to the problem, the sum of Wendell and Maggie's ages is 33, so we can write the first equation as Wendell's age + Maggie's age = 33. Next, we know that Wendell's age is three less than three times Maggie's age, so Wendell's age = 3*x - 3. Now, if we insert Wendell's age expression from the second equation into the first equation, we get 3*x - 3 + x = 33. When we solve this equation, we found that x equals to 9, hence, Maggie is 9 years old. That means, Wendell is 33 - 9 = 24 years old.
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Takiya recorded the heights of two sets of plants, one set planted in the shade and one set planted in full sun. Her data are shown in the plots below. A dot plot. A number line going from 1.5 to 4.5 in increments of 0.5 is labeled Heights of Shaded plants (inches). There are 0 dots above 1.5, 4 above 2, 3 above 2.5, 2 above 3, 0 above 3.5 and 4, and 1 above 4.5. A dot plot. A number line going from 1.5 to 4.5 in increments of 0.5 is labeled Heights of Full Sun plants (inches). There are 0 dots above 1.5, 1 above 2, 0 above 2.5, 2 above 3, 0 above 3.5, 4 above 4, and 3 above 4.5. Which best explains the variability of the sets? The shaded plants set has greater variability because more data is clustered around the median. The sets are equally variable because the ranges of the data sets are equal. The full sun plants set has greater variability because the IQR for full sun plants is greater. The full sun plants set has greater variability because the median for full sun plants is greater.
Answer:
c
Step-by-step explanation:
its not a b or d so its c
Answer: C
Step-by-step explanation: on edge
The original price of a shirt was $20. It was decreased to $15. What is the percent decrease of the price of this shirt?
Answer:
25%
Step-by-step explanation:
Price reduction = 20 - 15 = $ 5
Percent decrease of price = (5/20)*100 = 5*5 = 25%
What is the inner quartile range for 72,80,81,84,92,92,94,95?
Answer:
the inter quartile range is 12.5
Step-by-step explanation:
How is the graph of the parent quadratic function transformed to produce the graph of y=-(2x+6)? +3?
The graph is compressed horizontally by a factor of 2, shifted left 3 units, reflected over the x-axis, and translated up 3 units.
The graph is reflected over the x-axis, compressed horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.
The graph is stretched horizontally by a factor of 2, reflected over the x-axis, shifted left 3 units, and translated up 3 units.
The graph is reflected over the x axis, stretched horizontally by a factor of 2, shifted left 6 units, and translated up 3 units.
Answer:
d
Step-by-step explanation:
Answer:
B on ed
Step-by-step explanation:
got D wrong on ed so it is B
A cylindrical waste can has a volume of 5,667.7 cubic inches and its base has a radius of 9.5 inches. Find the height of the waste can. Round to the nearest tenth.
Answer:
20.0 inches
Step-by-step explanation:
The formula for the volume of a cylinder is useful here.
V = πr²h
Filling in the given numbers, we see ...
5667.7 = (3.14)(9.5²)h
Dividing by the coefficient of h, we get ...
h = 5667.7/283.385 = 20 . . . . inches
The height of the waste can is 20.0 inches.
_____
Comment on the solution
If you use a more exact value of pi, the height is closer to 19.9899 inches. It still rounds to 20.0.
volume of a sphere with a radius of 10
Answer:
4189 cubic units
Step-by-step explanation:
Put the value in the volume formula and do the arithmetic. The formula for the volume of a sphere is ...
V = (4/3)πr³
Filling in 10 for r, we have ...
V = (4/3)π(10³) = 4000π/3 ≈ 4189 . . . cubic units
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli and measure the weight of cheese filling. They find a sample mean weight of 15 grams with a standard deviation of 1.5 grams. What is the margin of error at 90% confidence?
A. 0.3 grams
B. 0.5133 grams
C. 0.8391 grams
D. 1.5 grams
E. 0.06 grams
Answer:
A.0.39 grams
margin of error at 90% confidence intervals is
M.E = 0.39 grams
Step-by-step explanation:
Explanation:-
Given a sample of size n = 25
mean of the sample x⁻ = 15 grams
Standard deviation of the sample 'S' = 1.5 grams
margin of error at 90% confidence intervals is determined by
[tex]Margin error = \frac{t_{0.90} S.D}{\sqrt{n} }[/tex]
The degrees of freedom ν = n-1 = 25-1 =24
The tabulated value t₀.₉₀ = 1.318
[tex]Margin error = \frac{1.318X 1.5}{\sqrt{25} }[/tex]
Margin of error = 0.3954
Conclusion:-
Margin of error at 90% confidence intervals = 0.3954
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 272 people entered the park, and the admission fees collected totaled 758.00 dollars. How many children and how many adults were admitted?
As an estimation we are told £3 is €4.
Convert €91.30 to pounds.
Give your answer rounded to 2 DP.
Answer:
68.48 pounds
Step-by-step explanation:
€91.30 to pounds
€91.30 * (3 pounds/ 4€) = 68.475 pounds about 68.48 pounds
A bakery sold 340 mocha cupcakes in a day, which was 85% of the total number of cupcakes sold that day. How many total cupcakes did the bakery sell that day?
Answer:
400
Step-by-step explanation:
Given:
Number of mocha cupcakes in a day = 340
Total number of cupcakes sold that day = [tex]85\%[/tex]
To find:
Total number of cupcakes sold by the bakery
Solution:
Let x denotes total number of cupcakes sold by the bakery.
According to question,
[tex]\frac{85}{100}x=340\\x=\frac{340}{85}\times 100=400[/tex]
So,
Total number of cupcakes sold by the bakery = 400
which cannot be a cross section of the figure? A cross section of the figure cannot be a ____
Answer: The answer is circle
Step-by-step explanation: The explanation is that you can see by looking at the shape you can easily make a rectangle, etc but you can not make a circle :).
Answer:
circle
Step-by-step explanation:
Help pleas this late
Answer:
V = 282.10 cm³
Step-by-step explanation:
[tex]V= \pi r^2\frac{h}{3}[/tex] Use this equation to find the volume of the cone
[tex]V=3.14(3.5)^{2} \frac{22}{3}[/tex] Simplify the (3.5)²
V = 3.14(12.25)(22/3) Multiply
V = 282.10 cm³
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The heights (in cm) and arm spans (in cm) of 31 students were measured. The association between (height) and (arm span) is shown in the scatterplot below. The equation of the line of best fit modeling this relationship is given:
y=4.5+0.977x
Mike is 172 cm tall and George is 165 cm tall. Using the model, how many centimeters longer would we expect Mike's arm span to be than George's? Round your answer to the thousandths place.
Answer: Mike's arm span is 7.165 cm longer than the George's one.
Step-by-step explanation:
We have that the association between height and arm span is modeled by the equation
y = 4.5 + 0.977*x
where y is height and x is arm span.
Mike is 172 cm tall, so his arm span is:
172cm = 4.5 + 0.977*x
x = (172 - 4.5)/0.977 = 171.443 cm
and George is 165 cm tall, so his arm span is:
x = (165 - 4.5)/0.977 = 164.278 cm
Then the difference between their arm span is:
171.443cm - 164.278cm = 7.165 cm
So Mike's arm span is 7.165 cm longer than the George's one.
What is the rate of change of the function shown in the table below
Answer: -3
Step-by-step explanation:
Answer:
-3
Step-by-step explanation:
A check is written pay to the order of Matthew Carter. Examine the check. For Mathew Carter, the check would be a . The amount would be the balance in his checking account.
Answer:The first one is deposit and the second one is added to.
Answer:
Deposit and Added To
Step-by-step explanation:
Jim had $2,052.24 in his checking account. He wrote a check to pay for
two airplane tickets. His account now has $1,084.12. How much did each
ticket cost? *
Answer:
$485.06
Step-by-step explanation:
Answer:
$484.06
Step-by-step explanation:
$2,052.24 - 1,084.12 = 916.12
916.12 divided by 2 = 484.06
Is 17,22,29 a right triangle
Answer:
No!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
formula:
a^2+b^2=c^2
Answer:
No
Step-by-step explanation:
The only way that those side lengths formed a right triangle is if they formed a pythagorean triple. [tex]\sqrt{17^2+22^2}=\sqrt{773}\neq 29[/tex]. Therefore, that is not a right triangle. Hope this helps!
which of the following statements are correct? select all that apply
Answer:
sorry, but you need to show the selectings
Step-by-step explanation:
Answer:
we cant see the choices
Step-by-step explanation:
For which value of x is the equation 6 = 12x true?
Answer:
x = 0.5
Step-by-step explanation:
The chart describes how four of Susan’s friends handle their money. Handling Money Person Description of Spending Sylvia She uses her whole paycheck to buy food and necessities and pay the minimum amount on her bills each month. Then, she buys new clothes and pays for them with a credit card. Nancy She uses her whole paycheck to buy food and necessities and then takes a trip each month, which she pays for by adding to a personal loan with her credit union. Fiona She buys food and necessities and pays more than the minimum due on her bills each month. She goes out with her friends using some of the money that is left over in her checking account. Uli She buys food and necessities and pays the minimum amount on her bills each month. She goes out with her friends using the money that is left over in her savings. Which person is most creditworthy? Nancy Sylvia Fiona Uli
Answer: C. Fiona
Step-by-step explanation: