a
Step-by-step explanation:
because it's is very important
A toy train set includes a train station building which is a scale model of a real building. The area of
the front side of the toy building is 1 square foot. The real building's front side has an area of 400
square feet. If we view the real building as a dilation of the toy, what is the scale factor?
Your answer
Answer:
[tex]20[/tex]
Step-by-step explanation:
The area of the front side of the toy model is [tex]1\ \text{ft}^2[/tex]
The area of the real building's front side is [tex]400\ \text{ft}^2[/tex]
So
[tex]1\ \text{ft}^2[/tex] of the toy model is equivalent to [tex]400\ \text{ft}^2[/tex] of the real building.
Area scale factor is given by [tex]k^2[/tex], where [tex]k[/tex] is the scale factor of the sides.
So,
[tex]\dfrac{400}{1}=k^2\\\Rightarrow k=\sqrt{400}\\\Rightarrow k=20[/tex]
Hence, the scale factor is [tex]20[/tex].
The scale factor should be 20.
Important information:The area of the front side of the toy building is 1 square foot. The real building's front side has an area of 400 square feet.
Calculation of the scale factor:Since 1 square foot should be equal to 400 square feet
So,
[tex]400\div 1 = k^2[/tex]
[tex]K = \sqrt{400}[/tex]
k = 20
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At the grocery store,
Ben purchased $7.50
worth of groceries and
a 44 cent stamp If he
paid with two $5 bills,
how much change
should he receive?
Answer:
$2.06
Step-by-step explanation:
add 7.05 and 44 cents. he used 2 5 dollar bills, which is 10 dollars. 10-7.94 is 2.06.
Your friend Fred claims that his average gym workouttime is at least 150 minutes per day. You pick a randomsample of 10 days and observe that on the days in thesample, Fred’s average workout time was 136 minutes.The standard deviation of workout times in the samplewas 28 minutes. You plan to use the sample results to testFred’s claim. Assume that Fred’s workout times are normally distributed.
Required:
Set up an appropriate hypothesis test to test Fred's claim. Use a significance level of 5%. Should Fred's claim be rejected? Explain.
Answer:
Step-by-step explanation:
Given that:
population mean = 150
Sample size = 10
Sample mean = 136
Standard deviation = 28
Significance level = 0.05
The null hypothesis:
[tex]H_o : \mu \ge 150[/tex]
The alternative hypothesis
[tex]H_a : \mu < 150[/tex]
This is a left-tailed test.
The t-test statistics can be computed as:
[tex]t = \dfrac{\overline x - \mu}{ \dfrac {s} {\sqrt{n}} }[/tex]
[tex]t = \dfrac{136 - 150}{ \dfrac {28} {\sqrt{150}} }[/tex]
t = -1.58
The P-value = P(t < -1.58)
Using the t tables
P-value = 0.0743
Decision rule: To reject the null hypothesis if the P-value is lesser than the level of significance.
Conclusion: We fail to reject the null hypothesis; since P-value is greater than (∝). Thus, there is sufficient evidence to support Fred's Claim.
No, we can not reject Fred's claim.
Help please What is the domain of the function
Answer: the first one
Step-by-step explanation:
A regular number cube is rolled. What is the probability that an odd number will not be rolled?
1/2,1/3,5/6,2/3,
Answer:
1/2
Step-by-step explanation:
A regular die has 3 odd numbers (1, 3, and 5) and 3 even numbers (2, 4, and 6). The question asks for the probability that an odd number will not be rolled. This is the same as asking the probability of an even number being rolled. Since we have 6 numbers in our data set and 3 are even, we can deduce that 1/2 of them are even and the probability of an even number being rolled is 1/2.
HTH :)
Answer:
the answer is 5/6
Step-by-step explanation:
Leslie’s employer will match up to 3% of her salary in contributions to her 401(k). Her monthly salary is $3,200, and the company allows her to make contributions to a maximum of 10% of her salary. What is the maximum monthly deposit to Leslie’s 401(k), including her employer’s matching contribution?
Answer:
$416.00
Step-by-step explanation:
Leslie's 10% and her employer's 3% total 13% of her salary:
0.13 · $3200 = $416
The maximum monthly deposit to Leslie’s 401(k) account, including her employer’s matching contribution, is $416.
What is a matching contribution?A matching contribution is a type of contribution that Leslie's employer decides to contribute to Leslie's 401(k) plan, which is an employer-sponsored retirement plan.
Data and Calculations:Monthly salary = $3,200
Leslie's maximum contribution = 10% of salary
Employer's matching contribution = 3% of salary
Total contributions to the 401(k) plan = 13% of salary
= $416 ($3,200 x 13%)
Thus, the maximum monthly deposit to Leslie’s 401(k) account, including her employer’s matching contribution, is $416.
Learn more about matching contributions at https://brainly.com/question/16338999
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Solve for the variable: a-9=-5
Solve for x.
3(-2x - 1) = 2(x + 5)
Answer:
x= − 8 /13 = −1 8 /5 = −1.625
Step-by-step explanation:
either one is the answer
<3 Enjoy,
Dea
Answer:
x=-1.625 Decimal form
x= -13/8 Fraction form
Step-by-step explanation:
3(-2x-1)=2(x+5)
Use distributive property to solve-
-6x-3=2x+10
Now add like terms
-6x-3=2x+10
+3 +3
-6x=2x+13 (get the x by itself)
-2x -2x
-8x=13 Divide
x= -1.625 Decimal form
x=-13/8 Fraction form
I need to find what's in those four boxes
Answer:
-500 + 200, -300
|0 - 200|, +200
Step-by-step explanation:
Kiran says that -2<-5. Do you agree with Kiran? Explain or show your reasoning.
Answer:
No I do not agree. -2 is closer to 0 than -5
Step-by-step explanation:
-5 -----------> -2---------> 0
A mathematical phrase represented by numbers, variables, and operations is a(n)
pls help:)
Answer:
Expression
Step-by-step explanation:
Answer: Expression
Got this right!!!
Hope this helps!!!
30% of 50. Find the percentage of the number.
Answer:
15
hope it's helpful ❤❤❤❤
THANK YOU.
Answer:
15
Step-by-step explanation:
30%x50÷100=15
determine the value of x if the measure of the sixth exterior angle of a hexagon is given by -6(3/16x-14)+3
Answer:
24°
Step-by-step explanation:
Assume the hexagon is regular.
how to integrate [tex]e^{2s} *Cos \frac{s}{4}[/tex] , please help, I have no idea what to do, I would appreciate if you show your work with steps.
Answer:
[tex]\int\limits {e^{2s} cos\frac{s}{4} ds[/tex] =[tex]\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s} ))[/tex]
Step-by-step explanation:
Step(i):-
Given that [tex]f(s) = e^{2s} cos\frac{s}{4}[/tex]
Now integrating
[tex]\int\limits {f(s)} \, ds = \int\limits {e^{2s} cos\frac{s}{4} ds[/tex]
By using integration formula
[tex]\int\limits { e^{ax} cos b x dx = \frac{e^{ax} }{a^{2}+b^{2} } ( a cos b x + b sin b x )[/tex]
Step(ii):-
[tex]\int\limits {e^{2s} cos\frac{s}{4} ds[/tex] = [tex]\frac{e^{2s} }{(2)^{2}+(\frac{1}{4}) ^{2} } ( 2 cos (\frac{1}{4} ) s + \frac{1}{4} sin \frac{1}{4} s ))[/tex]
= [tex]\frac{e^{2s} }{(4+\frac{1}{16})} ( 2 cos (\frac{1}{4} ) s + \frac{1}{4} sin \frac{1}{4} s ))[/tex]
= [tex]\frac{e^{2s} }{(\frac{65}{16} } ( \frac{8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s}{4} ))[/tex]
= [tex]16 X\frac{e^{2s} }{65 } ( \frac{8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s}{4} ))[/tex]
=[tex]\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s} ))[/tex]
Final answer:-
[tex]\int\limits {e^{2s} cos\frac{s}{4} ds[/tex] =[tex]\frac{4 e^{2s} }{65 } ({8 cos (\frac{1}{4} ) s + sin \frac{1}{4} s} ))[/tex]
Pablo shares 525 cupcakes in the ratio of 3 : 4 between his bakery and a supermarket.
How many cupcakes does the supermarket get?
Iuhi(in 6uguyguygugjhguygiygi6ihb
Answer:
gt676t6
Step-by-step explanation:
Answer:
yuhijokfdvbr9878r9t
Step-by-step explanation:
jy
10x-3Y=-150
how do you solve and graph?
a chicken eats 0.114 kg of grains per day. how much grain does the chicken eat in 31 days
Answer:
3.534kg
Step-by-step explanation:
0.114 × 31 = 3.534 kg
hope this helps...
8. There were 512 people at the Talent Show,
Admission was $1.25 for adults and 50
for children. The receipts were $406.75.
How many of each attended?
Answer:
7.9 of each
Step-by-step explanation:
Please help me i need it
Answer:
x+4x=5x
5x+x=6x
6x+8x=14x.
b - 1/8= 3 1/2
what’s b equal
7996
Ben sat outside his school in Cambridge and made a note of the colour of
the first 100 cars that passed.
27 of the cars were red.
In Britain there are around 35 million cars on the road .
Use bens findings to give an estimate of how many cars on the road are red
Answer:
1,296,296 cars are red.
A person riding in an elevator travels 180 feet in 30 seconds. What equation
represents this relationship? How many feet will the person travel in 10
seconds?
O A. y = 6x; 60 feet
O B. y = 6x; 6 feet
C. y = 82; 80 feet
O d. y= ; 17 feet
SUBMIT
PLEASE HELP!!!
Answer:
I believe its A
Tripp decided to go on vacation to the beach. After driving 60% of the way, he decided to stop for lunch. If he stopped for lunch after 240 miles of driving, how many total miles will he have to drive? Explain and/or show equation.
Answer:
40=10% im rightthe total is 400
Step-by-step explanation:
William fills 1/3 of a water bottle in 1/9 of a minute. How much time will it take him to fill the bottle
Answer:
3/9 = 1/3 of a minute or 20 seconds
Step-by-step explanation:
Answer:
1/3 of a minute
Step-by-step explanation:
1/3 x 3 = 1 bottle
1/9 x 3 = the time
1/9 x 3 = 3/9 or 1/3
PMI (Private Mortgage Insurance) protects the lender in case the borrower cannot make the loan payments. It is often required when the amount of the loan is close to the value of the home. PMI typically annually costs about .75% of the entire loan. On a $100,000 loan what would you be paying per month?
Answer:
$62.50
Step-by-step explanation:
The amount of private mortgage insurance required in this case per annum is 0.75% of the entire loan which is $100,000.
Annual insurance=0.75%*loan amount
Annual insurance=0.75%*$100,000
Annual insurance=$750
Since the annual cost of mortgage insurance per year is established, monthly cost would be annual cost divided by 12 months is which is number of months in a year that payments are to be made
monthly payment=$750/12
monthly payment=$62.50
Answer:
A
Step-by-step explanation:
Need help asap
Will mark you brainlist
△RST is shown below. XU = –2y + 15 and XW = 3y + 5.
PLEASE HELP ME
The required measure of the radius inscribed in the triangle RST is 11.
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
The incenter of the triangle will be the center of the circle inscribed in the triangle. and radius will be the perpendicular distance from the incenter to the sides.
So,
XU = XW,
-2y + 15 = 3y +5
5y = 10
y = 2
Now,
Radius = XU
= -2(2) + 15
= 11
Thus, the required measure of the radius inscribed in the triangle RST is 11.
Learn more about triangles here:
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Paul is a newspaper boy who received a total piecework
paycheck of $265.72. He receives 73 cents for every
newspaper he delivers. How many newspapers did he
deliver?
Answer:
364
Step-by-step explanation:
265.72 ÷ 0.73 is 364
Check:
364 x 0.73
265.72
Solve the inequality.
9p ≥ −72
Answer:
yes
Step-by-step explanation:
because of math,
Step-by-step explanation:
[tex] p\geqslant - 8[/tex]