Answer:
-39
Step-by-step explanation:
Sarah has two similar rectangular boxes. The dimensions of Box 1 are four times those of Box 2.
How many times greater is the surface area of Box 1 than the surface area of Box 2?
8
64
4
16
Answer:
16
Step-by-step explanation:
an area is always calculated by multiplying 2 dimensions.
when changing the dimensions, then the change factors for EACH dimension go into the calculation too.
therefore, when both dimensions of an area are enlarged 4 times, then the area is enlarged 4×4 = 16 times.
this just propagates to the whole surface area of an object, as each individual area of the overall surface area is enlarged by the same factor. and so, the sum of all the individual areas (= altogether the surface area of the object) is also enlarged in total by the same factor.
just think
16×a + 16×b + 16×c ... = 16×(a+b+c+...)
and you understand why.
Solve this inequality: 4x-8>-40
Answer:
x > - 8
Step-by-step explanation:
4x - 8 > - 40
4x > - 40 + 8
4x > - 32
Divide 4 on both sides,
4x / 4 > - 32 / 4
x > - 8
Which sequence is arithmetic?
O 2, 6, 18, 54, ...
O 3, 6, 12, 24, ...
O 11, 14, 17, 20, ...
O 7, 11, 13, 18, ...
Answer:
11, 14, 17, 20, ...
Step-by-step explanation:
An arithmetic sequence is one where each term increases by the same number every time. This is called the common difference and is always added to the previous term to get the current term. The only sequence that follows this is the third once. Every term increases by 3; therefore, it is an arithmetic sequence.
A certain drug is used to treat asthma. In a clinical trial of theâ drug, 17 of 258 treated subjects experienced headachesâ (based on data from theâ manufacturer). The accompanying calculator display shows results from a test of the claim that less than 11â% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.01 significance level to complete partsâ (a) throughâ (e) below. â
1-PropZTest
prop<0.11
z=â2.264337000
p=0.0117766978
p=0.0658914729
n=258
a. Is the testâ two-tailed, left-tailed, orâ right-tailed?
b. What is the best statistics?
c. What is the P-value?
d. What is the nut hypothesis and what do you conclude who det hypothesis?
Identify the null hypothesis.
A. H0: pâ 0.11.
B. H0: p=0.11.
C. H0: p<0.11.
D. H0: p>0.11.
Decide whether to reject the null hypothesis.
A. Reject the null hypothesis because theâ P-value is greater than α.
B. Fail to reject the null hypothesis because theâ P-value is less than or equal to α.
C. Reject the null hypothesis because theâ P-value is less than or equal to α.
D. Fail to reject the null hypothesis because theâ P-value is greater than α
e. What is the finalâ conclusion?
A. There is not sufficient evidence to warrant rejection of the claim that less than 11â% of treated subjects experienced headaches.
B. There is not sufficient evidence to support the claim that less than 11â% of treated subjects experienced headaches.
C. There is sufficient evidence to support the claim that less than 11â% of treated subjects experienced headaches.
D. There is sufficient evidence to warrant rejection of the claim that less than 11â% of treated subjects experienced headaches.
Solution :
a). The test is a left tailed test.
b). The sample proportion is :
[tex]$\hat p = \frac{x}{n}$[/tex]
[tex]$\hat p = \frac{17}{258}$[/tex]
= 0.065
Determining the Z statistics using the formula :
[tex]$Z=\frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]
[tex]$Z=\frac{0.065 - 0.11}{\sqrt{\frac{0.11(1-0.11)}{258}}}$[/tex]
= -2.31
∴ Z statistics value is -2.31
c). Using the excel function, the P-value is :
P-value = Normsdist(-2.31)
= 0.0104441
d). The null hypothesis is [tex]$H_0: P = 0.11$[/tex]
The level of significance is 0.01
We fail to reject the null hypothesis as the P value is less than or equal to the significant level.
Value of x
1\5(x)(1/5)=6/3(5/1)
Answer:
1/25=3/30
1250=
2501
2389
5552
Which equation shows a slope of 3 and a y-intercept of (0,7)?
y = 7x + 3
y = −7x + 3
y = 3x
y = 3x + 7
Answer:
[tex]{ \tt{y = 3x + 7}}[/tex]
Step-by-step explanation:
General equation of a line:
[tex]{ \boxed{ \bf{y = mx + c}}}[/tex]
m is the slope, and c is the y-intercept:
m = 3, and c = 7
PQRS is a parallelogram of area 18 cm. if PQ = 5 cm & QR = 4 cm. calculate the lengths of corresponding heights ?
Answer:
2cm
Step-by-step explanation:
area of parallelogram=b*h=18cm
5*4=20
length of corresponding heights=20-18
=2cm
the length of corresponding height of the parallelogram is : 2cm
Meaning of a parallelogramA parallelogram can be defined as a simple quadrilateral that is it possesses four sides and two pairs of parallel sides.
A opposite sides of a parallelogram are equal and the opposite angles of a parallelogram are equal.
In conclusion, the length of corresponding height of the parallelogram is : 2cm
Learn more about parallelogram : https://brainly.com/question/970600
#SPJ2
You are trying to get an important customer order out the door, but your boss keeps coming over to ask you about the status of this order and several other orders. He's just nervous and wants to be
Identify the triangle, ABC, which has a 72∘ angle and a 36∘ angle.
Answer:
isosceles acute
Step-by-step explanation:
sum of angles in a triangle = 180
to find third angle, subtract 72 & 36 from 180 and you get 72
72, 36, and 72 are all less than 90 so it will be an acute triangle
It will also be isosceles bc there are 2 angles of the same measure
If the average(arithmetic mean) of g and 100 is 75,what is the value of g + 100?
The value of g + 100 is 150.
Given that,
The average of g and 100 is 75.
And we have to determine the value of g + 100.
So that means
The arithmetic mean of g and 100 is 75.
So, mathematically it should be
[tex]\frac{g + 100}{2} = 75\\\\[/tex]
So, g + 100 = 150
Therefore we can conclude that the value of g + 100 is 150
Learn more about the mean here: brainly.com/question/11230531
I need help completing this problem ASAP
Answer:
D. [tex]3x\sqrt{2x}[/tex]
Step-by-step explanation:
The problem gives on the following equation:
[tex]\sqrt{32x^3}+-\sqrt{16x^3}+4\sqrt{x^3}-2\sqrt{x^3}[/tex]
Alongside the information that ([tex]x\geq0[/tex]).
One must bear in mind that the operation ([tex]\sqrt[/tex]) indicates that one has to find the number that when multiplied by itself will yield the number underneath the radical. The easiest way to find such a number is to factor the term underneath the radical. Rewrite the terms under the radical as the product of prime numbers,
[tex]\sqrt{2*2*2*2*2*x*x*x}-\sqrt{2*2*2*2*x*x*x}+4\sqrt{x*x*x}-\sqrt{2*x*x*x}[/tex]
Now remove the duplicate factors from underneath the radical,
[tex]2*2*x\sqrt{2x}-2*2*x\sqrt{x}+4x\sqrt{x}-2x\sqrt{x}[/tex]
Simplify,
[tex]4x\sqrt{2x}-4x\sqrt{x}+4x\sqrt{x}-x\sqrt{2x}[/tex]
[tex]3x\sqrt{2x}[/tex]
Find f′ in terms of g′
f(x)=x2g(x)
Select one:
f′(x)=2xf′(x)+2xg′(x)
f′(x)=2xg′(x)
f′(x)=2x+g′(x)
f′(x)=x2g(x)+2x2g′(x)
f′(x)=2xg(x)+x2g′(x)
f(x)g(x) if you find the derivative of two products, you get f(x)g’(x)+f’(x)g(x). Let’s say x^2 = f(x).
(x^2)(g’(x))+2x(g(x)) so it would be your last option, 2x(g(x))+x^2(g’(x))
Hello Pls help and thanks
Answer:
c.) in the correct answer
factorise m^2 - 12 m + 24
Answer:
(m-6+2root3)(m-6-2root3)
Step-by-step explanation:
m^2 - 12m +36 -12
= (m-6)^2 - 12
= (m-6+2root3)(m-6-2root3)[root 12 = 2root3]
Wyatt is making a salad using tomatoes, cucumbers, and carrots. This table gives the cost, per kilogram, of each ingredient, and the amount, in kilograms, that Wyatt uses:
Ingredient Price per kilogram Amount
Tomatoes 3.30dollars per kilogram 0.3
Cucumbers x dollars per kilogram y kilograms
Carrots z dollars per kilogram 0.20
The total amount Wyatt spends on ingredients is C dollars.
Write an equation that relates x, y, z, and C.
According to the given information, we build the equation for the cost. After we build the equation, the equation that relates these measures is:
[tex]C = 0.99 + xy + 0.2z[/tex]
Cost:
0.3 kilograms of tomatoes, at 3.30 dollars per kilogram.
Thus, the cost starts at:
[tex]C = 0.3*3.3 = 0.99[/tex]
y kilograms of cucumbers, at x dollars per kilogram.
Considering this, the cost will now be of:
[tex]C = 0.99 + xy[/tex]
0.2 kilograms of carrots, at z dollars per kilogram:
Now, we have to consider this for the cost, so:
[tex]C = 0.99 + xy + 0.2z[/tex]
A similar example is given at https://brainly.com/question/14544759
[tex]4 + \frac{4}{4 } \: = [/tex]
what is answer
Answer:
5Step-by-step explanation:
[tex]4 + \frac{4}{4} [/tex]
= 4 + 1
= 5 (Ans)
Consider a credit card with a balance of $7000 and an APR of 16.5 %. If you want to make monthly payments in order to pay off the balance in 1 year, what is the total amount you will pay? Round your answer to the nearest cent, if necessary.
9514 1404 393
Answer:
$7641.24
Step-by-step explanation:
The amortization formula tells the payment amount.
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where principal P is paid off in t years with n payments per year at interest rat r.
Using the given values, we find ...
A = $7000(0.165/12)/(1 -(1 +0.165/12)^-12) = $7000×0.01375/(1 -1.01375^-12)
A = $636.77
The total of 12 such payments is ...
$636.77 × 12 = $7641.24
You will pay a total of about $7641.24.
_____
Additional comment
Since the payment amount is rounded down, the actual payoff will be slightly more. Usually, the lender will round interest and principal to the nearest cent on each monthly statement. The final payment will likely be a few cents more than the monthly payment shown here.
find all points (x,y) that are 13 units away from the point (2,7) and that lie on the line x-2y=10
Answer:
(14,2) and (-6/5,-28/5)
Step-by-step explanation:
The distance, d, from two points (x,y) and another point (a,b) can be calculated using
d=sqrt((x-a)^2+(y-b)^2).
Our point (a,b) is (2,7) and d=13.
Making substitutions:
13=sqrt((x-2)^2+(y-7)^2)
We are also given the relation between x and y is given as x-2y=10.
Adding 2y to both sides gives: x=10+2y
Make this insertion into our equation:
13=sqrt((10+2y-2)^2+(y-7)^2)
Simplify inside:
13=sqrt((8+2y)^2+(y-7)^2)
Square both sides:
169=(8+2y)^2+(y-7)^2
Expand binomial squares:
169=64+32y+4y^2+y^2-14y+49
Combine like terms:
169=5y^2+18y+113
Subtract 169 on both sides:
0=5y^2+18y-56
We could try to factor
0=(5y+28)(y-2)
So y=2 or y=-28/5
Recall x=10+2y
So if y=2, then x=10+2(2)=10+4=14.
So if y=-28/5, then x=10+2(-28/5)=10+(-56/5)
=50/5 +-56/5
=-6/5.
So two points satisfying given criteria is
(14,2) and (-6/5,-28/5).
in figure , EF=1 and FC=2 What is the length of AC?
Step-by-step explanation:
ae=ec
ec=1+2=3
then ae=3
Answer:
6-most likely (AC=6)
Step-by-step explanation:
Because the 2 sides, AE and EC *look the same. Also you can look at the opposite sides.
*This is what I think
The product of two rational numbers is 47/42 and one of them is -11/21, find the other number
answer:
another number is -47/22
explanation:
let one number be x and the other be y
-11/21 × y = 47/42
y = -47/22
Answer:
- [tex]\frac{47}{22}[/tex]
Step-by-step explanation:
let n be the other number , then
- [tex]\frac{11}{21}[/tex] × n = [tex]\frac{47}{42}[/tex] ( divide both sides by - [tex]\frac{11}{21}[/tex] )
n = [tex]\frac{\frac{47}{42} }{-\frac{11}{21} }[/tex]
= [tex]\frac{47}{42}[/tex] × - [tex]\frac{21}{11}[/tex] ( cancel 21 and 42 )
= [tex]\frac{47}{2}[/tex] × - [tex]\frac{1}{11}[/tex]
= - [tex]\frac{47}{22}[/tex]
Angelica’s bouquet of a dozen roses contains 5 white roses. The rest of the roses are pink what fraction of the bouquet is pink? There are 12 roses in a dozen.
A. 5/12
B. 7/12
C. 5/7
D. 7/5
Answer:
7/12
Step-by-step explanation:
There are 12 roses - 5 white = 7 pink
7 pink / 12 total
*20 points*
how do you get the weighted average from this table?
Answer:
it is
[(2+3+4+6)-2*4]:4=1.75
I THINK
Step-by-step explanation:
Why wouldn't you use division to find an equivalent fraction for 7/15
Answer:
This depends whether you want to make the fraction bigger or smaller.
Step-by-step explanation:
If you want to the the fraction into something smaller than it already is, you would use division because when you divide something, you get a smaller number.
However, if you want to make the fraction bigger, then you would multiply.
Hope this helps! :)
Answer:
Because 7 is a prime number which means it can only divide by itself and one so you cannot divide seven but you can divide 15.
Step-by-step explanation:
John has a cylindrical propane tank that measures 8" in diameter and 8" tall If John
buys a new cylindrical propane tank that is twice as wide and half as tall as his
current tank, how much larger will the volume of the new tank be?
Answer:
2 times as large
Step-by-step explanation:
For the original cylinder, we can say that the volume of a cylinder is equal to V= πr²h. For this cylinder, we can say that V = π * radius² * height. The radius is equal to 1/2 of the diameter, so the original radius is 8/2 = 4. Therefore, the volume of the original cylinder is V = π * radius² * height = π * 4² * 8 = π * 16 * 8 = π * 128
For the new cylinder, "twice as wide" means that the diameter is twice as big as the original one. Half the height means that the height is halved. The new diameter is therefore 8 * 2 = 16 (meaning that the new radius is 16/2=8) while the new height is 8/2 = 4. The new volume is thus
V = π * radius² * height = π * 8² * 4 = π * 64 * 4 = π * 256
To see how much larger the new tank volume is, we can divide (new tank volume) by (old tank volume), resulting in
π * 256 / (π *128) = 2
Area of a circle whose circumference is 100ft
Answer:
A≈795.77ft²
Step-by-step explanation:
C=100ft
Area of circle=C^2/4pie
100/4×22/7≈795.77472ft²
△DOG ~△?
Complete the similarity statement and select the theorem that justifies your answer.
**If they are not similar, select "none" for both parts
9514 1404 393
Answer:
nonenoneStep-by-step explanation:
The reduced side ratios, shortest to longest are ...
AC : AT : CT = 8 : 9 : 15
OD : OG : DG = 5 : 6 : 10
These are different ratios, so the triangles are not similar.
Not sure how to do this
Twelve residents from the city of Rocklin were randomly selected and asked "How many TVs are in your household?". The following data were obtained: 2, 3, 3, 1, 2, 5, 3, 4, 1, 2, 4, and 3.
According to Nielsen Media Research the national average is 2.7 TVs per household. Is this sufficient sample evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average of 2.7 TVs per household? Use ! = 5% and assume that the number of TVs in Rocklin households is normally distributed.
Answer:
There isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average .
Step-by-step explanation:
This is a one sample mean test ;
H0 : μ = 2.7
H1 : μ > 2.7
Given the data :
2, 3, 3, 1, 2, 5, 3, 4, 1, 2, 4, 3
Sample size, n = 12
The sample mean, xbar = ΣX / n = 33/12 = 2.75
The sample standard deviation, s = 1.215 ( from calculator)
The test statistic :
(xbar - μ) ÷ (s/√(n))
T = (2.75 - 2.7) ÷ (1.215/√(12))
T = 0.05 / 0.3507402
T = 0.1426
The critical value from Tscore ;
df = 12 - 1 = 11
Critical value = 1.796
Since ; Test statistic < Critical value ;WE fail to reject the Null and conclude that there isn't enough evidence to indicate that the mean number of TVs in Rocklin households is higher than the reported national average
In the following problem, the ratios are directly proportional. Find the missing variable.
If y1 = 4, x2 = 6, and y2 = 8, what is the value of x1?
Answer:
x1 = 3
Step-by-step explanation:
first set up the proportion (write as fractions):
(y1/x1) = (y2/x2)
then fill in the variables:
4/x1 = 8/6
now cross multiply:
8 • x1 = 6 • 4
simple algebra:
8 • x1 = 24
x1 = 24/8
x1 = 3
If y1 = 4, x2 = 6, and y2 = 8, then the value of x1 is 3 which we can solve using ratios.
In a directly proportional relationship, the ratios between the corresponding values of two variables remain constant. This constant ratio is often referred to as the "proportionality constant."
In this problem, you have two pairs of values: (x1, y1) and (x2, y2). We're given that the ratios are directly proportional, which means:
x1 / y1 = x2 / y2
Plugging in the given values:
x1 / 4 = 6 / 8
Now, cross-multiply to solve for x1:
x1 * 8 = 4 * 6
x1 = 24 / 8
x1 = 3
Therefore, the value of x1 is 3.
Learn more about ratios here:
https://brainly.com/question/32531170?
#SPJ3
Mr. Cole packed 20 pounds into a suitcase, and Mrs. Cole packed 23 pounds into the same suitcase. They then had to remove 8 pounds because it was too heavy. How many pounds was their suitcase after making it lighter?
Answer:
35 lbs is the final weight
Step-by-step explanation:
20 +23 = 43 lbs
Then they had to remove 8 lbs
43 - 8 =35
35 lbs is the final weight
