Answer:
16 mi
Step-by-step explanation:
To find how many miles you could travel with one gallon, you want to multiply both sides of the equation by 64. This will make '1/64' to 1, so the answer should be 1/4 * 64 = 16.
Hannah and Zach together earn $950 for an
advertising drop. They earn equal hourly rates
of pay. If Hannah worked for 10 hours and
Zach for 9 hours, how much
did Zach earn?
Answer:
$450
Step-by-step explanation:
First, write out an equation. We know that Hannah and Zach together earnes $950 and they get payed in equal hourly rates, so for now, in this step of solving the problem, we will be adding the number of hours each person worked together.
Hannah worked 10 hrs and Zach worked 9 hrs, so add 10+9 to get 19 hrs worked in all between the two of them.
Let "x" represent the amount of money made each hour, and form your equation.
Your equation would be: [tex]19x=950[/tex]
Then, just solve for "x". Divide both sides by 19.
[tex]\frac{19x}{19}=\frac{950}{19}\\x=50[/tex]
The "x=50" means that Hannah and Zach each earn $50 per hour.
Now, the question asks us to find the amount of money that Zach made. So, multiply 50 by only the number of hours Zach worked, which is 9.
[tex]50*9=450[/tex]
That means that Zach made a total of $450.
simplify 2(3x+7)-4(7+x)
Answer:
[tex] \boxed{ \bold { \huge{ \boxed{ \sf{2x - 14}}}}}[/tex]
Step-by-step explanation:
[tex] \sf{2(3x + 7) - 4(7 + x)}[/tex]
Distribute 2 through the parentheses
⇒[tex] \sf{6x + 14 - 4(7 + x)}[/tex]
Distribute 4 through the parentheses
⇒[tex] \sf{6x + 14 - 28 - 4x}[/tex]
Collect like terms
⇒[tex] \sf{6x - 4x + 14 - 28}[/tex]
⇒[tex] \sf{2x + 14 - 28}[/tex]
Calculate
⇒[tex] \sf{2x - 14}[/tex]
Hope I helped!
Best regards!!
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{2(3x + 7) - 4(7 + x)}}\\\\{\mathsf{= 2(3x) + 2(7) - 4(7) - 4(x)}}\\\\\mathsf{= 6x + 14 - 28 - 4x}\\\\\mathsf{= (6x - 4x) + (14 - 28)}\\\\\mathsf{= 2x - 14}\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{2x - 14}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Which option shows the correct hypotheses for the test that the explanatory variables jointly significantly predict engine overhaul time?
Unclear question. However, I inferred you want to know about hypotehsis test.
Step-by-step explanation:
Remember, any hypothesis test is divided into two types. They are:
the null hypothesis andthe alternate hypothesis.Using this question example, here's the hypothesis statements ma sound:
Null hypothesis; There is a significant impact by the explanatory variables on engine overhaul time.
Alternate hypotheses; There is no impact by impact by the explanatory variables on engine overhaul time.
what is the slope of the line?
Answer:
Step-by-step explanation:
(1,15) and (2,30)
(30-15)/(2-1)= 15/1 = 15
How to do ii)
Deduce A^-1 = A^2 based on A^3=I
Multiply by [tex]A^{-1}[/tex] on the right of both sides of [tex]A^3=I[/tex], then use the fact that matrix multiplication is associative.
If [tex]A^3=I[/tex], then
[tex]A^3A^{-1}=IA^{-1}[/tex]
[tex]A^2(AA^{-1})=A^{-1}[/tex]
[tex]A^2I=A^{-1}[/tex]
[tex]\implies A^2=A^{-1}[/tex]
James works in a post office and is paid $8 per hour. Last week, he worked
32 hours and this week he worked 33.25 hours. How much should his
biweekly (every 2 weeks) paycheck be for?
Answer:
James will receive a paycheck in the amount of $522.
Step-by-step explanation:
There are 2 ways you can go at finding the answer. The first way is by adding 32 hours and 33.25 hours together to get a total of 65.25 hours. Then multiply 65.25 hours by $8 to get $522. The second way is multiplying 32 hours by $8 and get $256. Then multiply 33.25 hours by $8 to get $266. Finally add $256 and $266 up and you get $522. I hope this helps you!
What is 0.000345 expressed in scientific notation?
O 3.45 x 102
O 3.45 x 10
0 3.45 x 102
0 3.45 x 10 4
Answer:
The answer is D 10 to the power of -4.
Step-by-step explanation:
When the decimal point moves left, the power of becomes negative. Therefor the answer is D.
Have a good day.
what is the formula for the area of a triangle?
a. a^2 + b^2 = c^2
b. A= 1/2acosB
c. A= 1/2bcsinA
d. a^2 = sin^2 + cos^2c
Answer: c. (1/2) bc sin A
Step-by-step explanation:
You can find the area of a triangle using trigonometry if you know the lengths of two sides and the measure of the included angle using the following formula:
[tex]A=\dfrac{1}{2}ab\sin C[/tex]
Answer:
[tex]\Large \boxed{\mathrm{\bold{C} }}[/tex]
Step-by-step explanation:
We can find the area of the triangle when two sides are given and the angle in between the two sides.
[tex]\displaystyle A=\mathrm{\frac{1}{2} bc \cdot sinA}[/tex]
b and c are the sides and A is the angle in between b and c.
For the diagram, calculate; the radius of the smaller section and the perimeter of the shape of the and;
Answer:
a). Radius r of the small sector= 12cm
b). Perimeter of the shape= 68 cm
c). Angle= 47.7°
Step-by-step explanation:
a). Radius of the big sector= 24 cm
Arc if the big sector= 20 cm
Arc of the small sector= 10 cm
For the radius r of the small sector
r/10 = 24/20
r=(10*24)/20
r= 24/2
r= 12 cm
Radius r of the small sector= 12cm
b). Perimeter of the shape
= Total length of the shape
Let's note that the other side of the sector is also the radius= 24 cm
Perimeter= 20+24+24
Perimeter of the shape= 68 cm
c) the angle
Length of arc = 2πr*(angle/360)
Let angle = b
Length of arc = 20cm
20= 2*3.14*24*(b/360)
(20*360)/(2*3.14*24)= b
47.7°= b
Angle= 47.7°
A = 1 −7 −1 2 , B = 3 7 −1 0 , C = 1 0 −1 1 Find: a) BC, b) 5A − 2C, c) A + C,
Answer:
b
Step-by-step explanation:
Let x stand for the length of an individual screw. 100 screws were sampled at a time. The population mean is 2.5 inches and the population standard deviation is 0.2 inches. What is the mean of the sampling distribution of sample means?
a) 0.2
b) 2.5
c) 0.02
d) 2.
Answer:
The correct option is b
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 100[/tex]
The population mean is [tex]\mu = 2.5[/tex]
The sample standard deviation is [tex]\sigma = 0.2[/tex]
Generally the mean of the sampling distribution of sample means is mathematically represented as
[tex]\mu_{\= x } = \mu[/tex]
=> [tex]\mu_{\= x } = 2.5[/tex]
The price of a cup of coffee was $2.10 yesterday. Today, the price rose to $2.25. Find the percentage increase. Round your answer to the nearest tenth
of a percent.
Answer:
Easy-peasy.
Step-by-step explanation:
2.45/2.10 = 1.167 (rounded to the nearest tenth of a cent).
That is, 2.45 is 116.7% of 2.10
Since $2.10 is 100% of 2.10,
2.45 is a 16.7 increase.
The solution is 7.1 %
The percentage increase in the price of the coffee is 7.1 %
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
Let the percentage increase in the price of the coffee be represented as A
Now , the value of A is calculated by
Let the initial price of the coffee be = P
The value of P = $ 2.10
The increased price of the coffee be = Q
The value of Q = $ 2.25
Now , the equation will be
The percentage increase in the price A = ( increased price of the coffee - initial price of the coffee / initial price of the coffee ) x 100
Substituting the values in the equation , we get
The percentage increase in the price A = ( ( 2.25 - 2.10 ) / 2.10 ) x 100
The percentage increase in the price A = ( 0.15 / 2.10 ) x 100
The percentage increase in the price A = 0.0714 x 100
The percentage increase in the price A = 7.14 %
Therefore , the percentage increase is 7.1 %
Hence , the percentage increase in the price is 7.1 %
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pls someone help me
Answer:
C
Step-by-step explanation:
Starting at zero, it went back 2/5 to negative 2/5. Then it went forward 4/5 to positive 2/5, which is the answer.
I need help with the following questions. Help would be very much appreciated! :D
Step-by-step explanation:
a) 12:40 = 3: 10
b) 40:12 = 10:3
c)
[tex]1. \: \frac{non \: fiction}{graphic \: novels} [/tex]
[tex]2. \: \frac{science \: fiction}{graphic \: novels} \: \: \: \: \: \: \: 3. \frac{science \: fiction}{non \: fiction} [/tex]
d)
Fiction books is 80.
Many smoke detectors contain:
A. Carbon-14
B. Americium-241
C. Strontium-90
D. Iodine
Answer:
Option B, Americium-241, is the right answer.
Step-by-step explanation:
A device which senses smoke usually as an indicator of fire is known as a smoke detector.The two most common types of smoke detectors are the Ionization chamber and photoelectric smoke indicators. Many of these smoke detectors comprise some amount of americium-241, which is a radioactive substance. These smoke detectors respond immediately to fires that give off some smoke.
If 3s = t + 5 and s
= 4, then t = ?
3s=t+5
s=4
we substitute 4 for s in the equation
3*4=t+5
12=t+5
t=12-5
t=7
Answer:
Brainliest!
Step-by-step explanation:
3s = t+5
s = 4
so...
3 (4) = t+5
12 = t+5
t = 7
The square of a number is 3 less than four times the number. Which values could be the number?
Answer:
The numbers are 1 and 3Step-by-step explanation:
Let the number be x
The statement
The square of a number is 3 less than four times the number is written as
x² = 4x - 3
Solve the quadratic equation
We have
x² - 4x + 3 = 0
Write - 4x as a difference
That's
x² - x - 3x - 3 = 0
Factorize the expression
That's
x( x - 1) - 3( x - 1) = 0
( x - 1)( x - 3) = 0
x - 1 = 0 x - 3 = 0
x = 1 x = 3
The numbers are 1 and 3
Hope this helps you
Answer:
1 and 3
Step-by-step explanation:
Consider the following repeating decimal. 0.619
(a) Write the repeating decimal as a geometric series.
0.619 = _______ + n=0 summation infinity _______
(b) Write the sum of the series as the ratio of two integers
Answer:
a. 0.6[tex]\overline {19}[/tex] = [tex]0.6 + \ \sum \limits ^{\infty}_{n=0} \ 0.019 \ ( \dfrac{1}{100})^n[/tex]
b. 0.6[tex]\overline {19}[/tex] = [tex]\mathbf{\dfrac{613}{990}}[/tex]
Step-by-step explanation:
Consider the following repeating decimal. 0.6[tex]\overline {19}[/tex]
a) Write the repeating decimal as a geometric series.
0.6[tex]\overline {19}[/tex] is being expressed as 0.6191919...
0.6[tex]\overline {19}[/tex] = 0.6 + 0.019 + 0.00019+ 0.0000019 + ...
0.6[tex]\overline {19}[/tex] =[tex]0.6 + \dfrac{19}{1000}+ \dfrac{19}{100000}+ \dfrac{19}{10000000}+ ...[/tex]
0.6[tex]\overline {19}[/tex] = [tex]0.6+ \dfrac{19}{1000} \begin {bmatrix} 1 + \dfrac{1}{100} + \dfrac{1}{10000}+ ... \end {bmatrix}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]0.6 + \ \sum \limits ^{\infty}_{n=0} \ 0.019 \ ( \dfrac{1}{100})^n[/tex]
(b) Write the sum of the series as the ratio of two integers
0.6[tex]\overline {19}[/tex] = [tex]0.6 + 0.019 ( \dfrac{1}{1-0.01})[/tex]
0.6[tex]\overline {19}[/tex] =[tex]0.6 + \dfrac{19}{1000}\times \dfrac{100}{99}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]0.6 + \dfrac{19}{990}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]\dfrac{594+19}{990}[/tex]
0.6[tex]\overline {19}[/tex] = [tex]\mathbf{\dfrac{613}{990}}[/tex]
If half of a box of candy weighs 3/5 of a pound, how much would 4 full boxes weigh?
If 3s = t + 5 and se = 4, then t =
Answer:
t must be 7
Step-by-step explanation:
Replace s with 4 and solve for t in the original equation:
3 s = t + 5
3 (4) = t + 5
12 = t + 5
12 - 5 = t
7 = t
So t must be 7
Find the value of x. Picture below
Answer:
x=6
Step-by-step explanation:
BD is bisecting of <B
x/3=8/4 the theorem of the bisecting
4*x=3*8
4x=24
x=24/4
x=6
What is the solution set of the equation 2z+6z+2=3−1z
Note: z≠0,−2
Answer:
z = 1/9
Step-by-step explanation:
2z + 6z + 2 = 3 - 1z
2z + 6z + 1z = 3 - 2 (on rearranging)
9z = 1 (on solving)
z = 1/9
HOPE IT HELPS (✿^‿^)
Six-four million, one hundred eighty-six thousand, three hundred square miles in standard form
Answer:
64,186,300 square miles
I'm sorry if I misunderstood.
Good luck mate! :)
Please add Brainliest if you'd like, not that it matters.
Remember to try your best every day!
Find the product. (3p–2)(2p^2–p+3)
Answer:
6p^3−7p^2+11p−6
Step-by-step explanation:
1. You would want to foil it, which means multiplying one number from each parentheses to the next parentheses, like so:
3p * 2p ^ 2 = 6p^3
3p * -p = -3p
3p * 3 = 9p
-2 * 2p^2 = -4p^2
-2 * -p = 2p
-2 * 3 = - 6
2. Now add all of the numbers we foiled together, thus getting you:
6p^3−7p^2+11p−6
Dione has 3 rolls of pennies containing 50 coins each, 4 rolls of nickels
containing 40 coins each, 5 rolls of dimes containing 50 coins each, and 6
rolls of quarters containing 40 coins each. How much money does she have?
Answer:
$94.50
Step-by-step explanation:
3(50)=150 $1.50
4(40)=160 160(5)=800 $8.00
5(50)=250 250(10)=2500 $25.00
6(40)=240 240(25)=6000 $60.00
60+25+8+1.5=$94.50
Question 4
Given the following definitions:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4,5)
B = {1, 3, 5, 7)
How many elements are in A u B?
Answer:
A union B = { 1, 2, 3, 4, 5, 7 }
The A∪B will be {1,2,3,4,5,7}. Then the number of the terms in A∪B will be 6.
What are Sets?Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.
The union of A and B is given as all the terms in A and B.
Given the following information:
U = {1, 2, 3, 4, 5, 6, 7}
A = {1, 2, 4,5)
B = {1, 3, 5, 7)
Then the A∪B will be given as,
A∪B = 6{1, 2, 3, 4, 5, 7}
Thus, the A∪B will be {1,2,3,4,5,7}.
Then the number of the terms in A∪B will be 6.
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i need help asap !!!!!!!!!!!
Answer:
3 a : YES
3 b : NO
4:
F
D
E
5:
IH
GH
IG
Step-by-step explanation:
3 a) Yes The sum of any two sides is larger than the third side
3 b). NO The sum of 3 ft + 4 ft gives 7ft which is not larger than 10 ft
4 Recall that larger angles opposite larger sides, and smaller angles oppose smaller sides in the triangle. Therefore, the smallest angle must be that opposite the 1 1/4 side that is angle [tex]\angle F[/tex] then angle d must follow (opposes side of length 2) and lastly angle E (since it opposes the largest side of length 2 1/8
5:
Notice that the third angle which is not given must verify the following:
[tex]\angle I = 180^o-59^o-61^o=60^o[/tex]
Therefore following the same concept as explained in the previous problem the order of these angles from smallest to largest must be:
IH
GH
IG
A manufacturer claims that the calling range (in feet) of its 900-MHz cordless telephone is greater than that of its leading competitor. A sample of 9 phones from the manufacturer had a mean range of 1260 feet with a standard deviation of 24 feet. A sample of 12 similar phones from its competitor had a mean range of 1230 feet with a standard deviation of 37 feet. Do the results support the manufacturer's claim? Let μ1 be the true mean range of the manufacturer's cordless telephone and μ2 be the true mean range of the competitor's cordless telephone. Use a significance level of α=0.1 for the test. Assume that the population variances are equal and that the two populations are normally distributed.
a. State the null and alternative hypotheses for the test.
b. Compute the value of the t test statistic. Round your answer to three decimal places.
c. Determine the decision rule for rejecting the null hypothesis H0. Round your answer to three decimal places.
d. State the test's conclusion.
Answer:
a
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex] (Manufacturers claim)
b
[tex]t = 2.114[/tex]
c
Decision rule
Reject the null hypothesis
d
There is sufficient evidence to support the claim that the calling range (in feet) of Manufacturers 900-MHz cordless telephone is greater than that of its leading competitor
Step-by-step explanation:
From the question we are told that
The first sample size is [tex]n_1 = 9[/tex]
The second sample size is [tex]n_2 = 12[/tex]
The first sample mean is [tex]\= x_1 = 1260 \ feet[/tex]
The second sample mean is [tex]\= x_2 = 1230[/tex]
The first standard deviation is [tex]\sigma_1 = 24[/tex]
The second standard deviation is [tex]\sigma_2 = 37[/tex]
The significance level is [tex]\alpha = 0.10[/tex]
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 \le 0[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 > 0[/tex] (Manufacturers claim)
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 -2[/tex]
[tex]df = 9 + 12 - 2[/tex]
[tex]df = 19[/tex]
Generally the pooled standard deviation is mathematically represented as
[tex]\sigma_p = \sqrt{ \frac{(n_1 - 1)\sigma_1^2 + (n_2-1 )\sigma_2^2 }{ (n_1 - 1 ) + (n_2 - 1 )} }[/tex]
[tex]\sigma_p = \sqrt{ \frac{(9 - 1)24^2 + (12-1 )37^2 }{ (9 - 1 ) + (12 - 1 )} }[/tex]
[tex]\sigma_p =32.17[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x_1 - \= x_2 }{\sqrt{\frac{\sigma_p^2}{n_1 } +\frac{\sigma_p^2}{n_2 } } }[/tex]
[tex]t = \frac{1260 - 1230 }{\sqrt{\frac{32.17^2}{9 } +\frac{32.17^2}{12 } } }[/tex]
[tex]t = 2.114[/tex]
Generally the p-value is obtained from the student t distribution table and the value is
[tex]p-value = P(t > 2.11) = t_{2.11 , 19} = 0.024173[/tex]
Given that the [tex]p-value < \alpha[/tex]
The null hypothesis is rejected
Hence we can conclude that there is sufficient evidence to support the claim that the calling range (in feet) of Manufacturers 900-MHz cordless telephone is greater than that of its leading competitor
Tyrion can invest in an account earning 2.5% interest compounded monthly. If he invests $5000, ow much will he have in 7 years?
Answer:
$5925.51Step-by-step explanation:
We are going to be using the compound interest formula
Given data
principal P= $5000
N is time = 7 years
rate r= 2.5%= 0.025
compounded monthly k= 112
final amount A=?
The expression for the compound interest is
[tex]A= P(1+\frac{r}{K} )^K^N[/tex]
substituting into the expression we have
[tex]A= 5000(1+\frac{0.025}{12} )^1^2^*^7\\\\ A= 5000(1.002 )^1^2^*^7\\\\ A= 5000(1.002 )^8^7\\\\A= 5010*1.18273815853 \\\\ A= 5925.51[/tex]
in seven years he will have $5925.51
The following table shows a proportional relationship between xxx and yyy. xxx yyy 222 999 555 22.522.522, point, 5 888 363636 Write an equation to describe the relationship between xxx and yyy.
Answer:
y=4.5x
Step-by-step explanation:
I got it correct on Khan!
Hope this helps ;)
The equation that describes the proportional relationship between x and y is: y = 4.5x.
How to Write the Equation of a Proportional Relationship?To write the equation of a proportional relationship between variables x and y, find the constant of proportionality, which is k = y/x, then plug in the value of k into y = kx.
Constant of proportionality (k) = 9/2 = 22.5/5 = 36/8 = 4.5
Substitute k = 4.5 into y = kx.
y = 4.5x.
The equation is: y = 4.5x.
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