Answer:
Given - Twice a no. is 42 less than 5 times a no.
To find - The no.
Solution -
Let the no. be XAccording to the question the equation made is -
2x = 5x - 42
2x - 5x = (-42)
(-3x) = (-42)
x= (-42)/(-3)
x = 14
The no. is 14
Indicate the answer choice that best completes the statement or answers the question.
✓ The table shows the cost of long distance calls as a function of the number of minutes used. Is the cost a linear or nonlinear function of the
number of minutes used? Explain.
Number of Minutes 40 180 120 160 1200
Cost (S)
14.00 8.00
16.00 20.00
12.00
Answer:
The correct answer is:
Option C: Linear; as x increases by 40 minutes and y increases by $4 each time. The rate of change is constant, so this function is linear.
Step-by-step explanation:
Given is the table,
The input is x and output is y.
We can see from the table that the x-values are increasing 40 minutes after each input and the output is increasing by equal amount i.e. $4.
The rate of change remains the same.
Hence,
The correct answer is:
Option C: Linear; as x increases by 40 minutes and y increases by $4 each time. The rate of change is constant, so this function is linear.
Find the square
X^2+2x=35
Answer:
x=-7,5
Step-by-step explanation:
What is the image point of (-7, 4) after translation left 3 units and up 5 units
Answer:
(-2,1)
Step-by-step explanation:
up and right is adding to the current point so (-7+5,4)
down and left is subtracting to the current point so (-2,4-3)
If you combine them, you get: (-7+5,4-3)-which is (-2,1)
Simplify using the laws of exponets.
Answer:
2*5
Step-by-step explanation:
when youre dividing with powers you have to subtract them so 2*5-2*4=2*1. When the power is in brackets you multiply the whole power. So 2*1 x 5 = 2*5.
A store has apples on sale for $14.00 for 4 pounds. If an apple is approximately 5 ounces, how many apples can you buy for $56.00? Complete the explanation.
Answer:
51.2 apples, but obviously you can't do that, so i think the answer would be 51 apples
Step-by-step explanation:
y=2 |x|
(where do I graph it? HELP
Answer:
The graph should help :)
Kate Sanders, a researcher in the department of biology at PFW University, studied the effect of agricultural contaminants on the stream fish population in northeastern Indiana (April 2012). Specially designed traps collected samples of fish at each of four stream locations. A research question was: did the differences in agricultural contaminants found at the four locations alter the proportion of the fish population by gender
Full question attached
Answer and explanation:
Null hypothesis : all population proportions are equal, p1=p2=p3=p4
Alternative hypothesis : Not all population proportions are equal
To find our p-value using chi Square method, we first find expected frequencies from observed frequencies above
Expected Frequencies:
Gender A. B. C. D
Male. 46.81 46.81 44.21 43.17
Female 43.19. 43.19 40.79 39.83
Total = 348
chi Square for table = (observed frequency - expected frequency)²/expected frequency
Gender. A. B. C. D
Male. 0.10 0.17 0.52 0.40
Female 0.11 0.18 0.56 0.44
x²= 2.49
Degrees of freedom(df)= k – 1 = (4 – 1) = 3
Using the chi Square table with degree of freedom = 3, 2 and x²= 2.49 shows, the p –value = 0.4771 therefore we do not reject null hypothesis since p value is greater than significance level 0.08
We do not reject the null hypothesis
b. There is no evidence of differences in proportion
What postulate/theorem can be used to prove the following triangles congruent?
Answer: SAS
Step-by-step explanation:
It is given that the two sides are congruent.
The angle between the two congruent sides is also congruent because of the vertical angle theorem.
Since a side, angle, and side are congruent, the theorem is SAS.
What is 82.403 rounded to the nearest whole number
Answer: 82
Step-by-step explanation:
Which expressions are factors of the expression
-24xyz - 12xy + 20xyz
Answer:
xy
2xy
4
Step-by-step explanation:
A factor is a number of term you can factor out of each part of the expression/ or divide it by.
In -24xyz - 12xy + 20xyz
All three parts have xy, so it is a factor
All three don't have 12xz, because -12xy doesn't have z variable for instance.
All three have 2xy.
All three can't factor out 3y, because you can't divide 20 by 3 nicely.
All three can't factor out 4yz, because middle term -12xy doesn't have z.
All three can't factor out 12, because you can't nicely divide 20/12.
All three can factor out 4, because -24, -12, and 20 are all divisible by 4.
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The area of a square is 144 cm' and one of
its sides is (x + 2) cm. Find x and then theside of the square
Answer:
The side of the square is 12 cm and x = 10 cm.
Step-by-step explanation:
Since it's a square, it's sides have the same length.
Hence, since one of it's sides is x + 2, the other side must be x + 2 as well.
Therefore, we can set up an equation:
[tex](x + 2)^{2} = 144 cm^{2}[/tex]
[tex](x + 2) = \sqrt{144cm^{2}}[/tex]
[tex]x + 2 = 12 cm[/tex]
[tex] x = 10 cm[/tex]
Hence, the side of the square is 12 cm and x = 10 cm.
Hope this helped!
Answer this ASAP please. If you can’t see then zoom in. Giving out 25 points and Brainliest to the one who answers correctly. There is a PT2 to this, so you’ll have another chance to answer if you want.
Thank you in advance.
Answer:
Put 2 feet down for both of them and add 3 extra feet for nate
Step-by-step explanation:
Answer:
add 3 extra feet for Nate and put 2 feet from the both of them
Step-by-step explanation:
find the scale factor of the dilation
Answer:
k=1/2
It is a reduction
Step-by-step explanation:
To the scale factor, you simply divide the length of the post image by the image.
10/20=k
1/2=k
A reflector on the inside of a certain flashlight is a parabola given by the equation y = x2– 25. Find the points where
the reflector meets the lens by finding the values of x when y = 0.
Answer:
[tex]\boxed{x_1 = 5~~or~~x_2 = -5}[/tex]
.
Step-by-step explanation:
[tex]\to y = 0[/tex]
[tex]y = x^2 - 25[/tex]
[tex]x^2 - 25 = 0[/tex]
[tex]x^2 = 25[/tex]
[tex]x = \pm \sqrt{25}[/tex]
[tex]x = \pm 5[/tex]
.
[tex]x = 5[/tex]
[tex]x = -5[/tex]
The point where the reflector meets the lens is ± 5.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
Given, A reflector on the inside of a certain flashlight is a parabola given by the equation y = x² - 25.
Now the points where the reflector meets the lens are,
0 = x² - 25.
x² = 25.
x = ± 5.
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If a line crosses the y-axis at (0, 1) and has a slope of 4/5 , what is the equation of the line?
ОА.
4y-5x=5
OB.
y- 4x = 5
O C.
5y + 4x = 5
OD. 5y - 4x = 5
I need help
24) A hotel contains 180 rooms divided equally among a number of floors, each floor
contains 15 rooms. How many floors are there in this hotel?
Answers please, and will this be multiplication or division?
Answer:
Well 180 divided by 15 is 12 so that said there would be 12 floors
So
1 floor 15
2 floor 30
3 floor 45
4 floor 60
5 floor 75
6 floor 90
7 floor 105
8 floor 120
9 floor 135
10 floor 150
11 floor 165
12 floor 180
Hope that helps
A survey of nonprofit organizations showed that online fundraising has increased in the past year. Based on a random sample of 133 nonprofits, the mean one-time gift donation resulting from email outreach in the past year was $85. Assume that the sample standard deviation is $9. Identify the correct 95% confidence interval estimate for the population mean one-time gift donation.
Answer:
The answer is below
Step-by-step explanation:
Given that:
Confidence interval (C) = 95%, mean (μ) = 85, standard deviation (σ) = 9, sample size (n) = 133
α = 1 - C = 1 - 0.95 = 0.05
α/2 = 0.025
The z score of α/2 (0.025) is the same as the z score of 0.475 (0.5 - 0.025) which is equal to 1.96.
The margin of error (E) is given as:
[tex]E=Z_\frac{\alpha}{2}*\frac{\sigma}{\sqrt{n} } \\\\E=1.96*\frac{9}{\sqrt{133} } \\\\E=1.53[/tex]
The confidence interval = (μ ± E) = (85 ± 1.53) = (83.47, 86.53)
The confidence interval is between 83.47 and 86.53.
Which of the following MUST be true for two negative number?
There is n arithmetic means between 2 and 46 such that the first mean: last mean is 1:7. find the value of n.
Answer:
n = 10Step-by-step explanation:
The nth term of an arithmetic sequence is expressed as:
Tn = a + (n-1)d
a is the first term
n is the number of terms
d is the common difference
Let the sequence be 2, T1, T2, T3...Tn, 46
The common difference is expressed as d = b-a/n+1
T1 = 2 + d
Given b = 46 and a = 2
d = 46-2/n+1
d = 44/n+1
T1 = 2 + (44/n+1)
T1 = 2(n+1)+44/n+1
T1 = 2n+2+44/n+1
T1 = 2n+46/n+1
Similarly;
Tn = 2 + nd
Tn = 2 + n(44/n+1)
Tn = 2 + 44n/n+1
Tn = 2(n+1)+44n/n+1
Tn = (2n+2+44n)/n+1
Tn = 46n+2/n+1
If the ratio of the first mean to last mean is 1:7 then T1/Tn = 1/7
(2n+46/n+1)÷(46n+2/n+1) = 1/7
2n+46/n+1 * n+1/46n+2 = 1/7
2n+46/46n+2 = 1/7
Cross multiply and solve for n:
46n + 2 = 7(2n + 46)
46n + 2 = 14n + 322
46n - 14n = 322-2
32n = 320
n = 320/32
n = 10
Hence the value of n is 10
Rewrite the equation 8r+62 - 7 = 2 in standard form and Identify a, b, and c
Answer:
a = 0
b = 8
c = 53
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Algebra I
Standard Form: ax² + bx + c = 0Step-by-step explanation:
Step 1: Define
8r + 62 - 7 = 2
Step 2: Rewrite
Add: 8r + 55 = 2Subtract 2 on both sides: 8r + 53 = 0Step 3: Identify Variables
a = 0
b = 8
c = 53
Please help me thank you so much I appreciate it
Answer:
12
Step-by-step explanation:
To find perimeter, add the lengths of each side. 5 + 4 + 3 = 12
Answer:
12
Step-by-step explanation:
5+4+3
Which expressions represent the distance between-1 and 4? Choose ALL that apply. 14 - 11 | 4 – (-1) HH34 4342 0 3 5 |-1 - 4 |-1 - (-4)
Hope watches a movie Friday night that was two and one-half hours long. On Saturday, she watched a documentary half as long as Friday’s movie. How long was the documentary?
Answer:
1 hour and 15 minutes thats how long the documentary was
Movie friday night was 2 hours and 30 minutes long.
The documentary was half as long as Friday's movie.
So it will be: [tex]\frac{2 hours .and. 30 minutes}{2} = 1 hour.and .15 minutes[/tex]
Landon bought a tray of plants for $8.15. There were 16 plants in the tray. If Landon only bought 1 plant, about how much would it have cost?
Triangle ABC has vertices A (2, 4), B(0, -4),
and C(-2,-2). It is dilated about the origin
to form triangle A'B'C' with vertices
A' (12, 24), B (0, -24), and C (-12, -12).
What is the scale factor of the dilation?
Answer:
k=6
Step-by-step explanation:
To find the scale factor of a triangle, all you have to do is divide the image from the post image
point A
12/2=6
24/4=6
The scale factor is 6
Suppose that in one week in November in St. Louis, the temperature dropped by an average of 4 degrees every day. The temperature at the beginning of the week was 65 degrees. Write an equation that relates the temperature (t) to the number of days that have passed (d). helpppp
Answer:
t = 65 - 4d
Step-by-step explanation:
Linear Modeling
The temperature in St. Louis dropped by 4 degrees every day in one week.
When d days have passed, the temperature will have dropped by 4d degrees.
We know the temperature t at the beginning of the week was 65 degrees.
Thus, when d days pass, the linear model for the temperature t is:
t = 65 - 4d
greatest number which divides into 304 to leave
remainder of 4 and which also divides into 298 to leave a remainder of 4.
Answer:
answer is 6
Step-by-step explanation:
Integrate the following problem:
[tex]\int {e^{-x} \cdot cos(2x)} \, dx[/tex]
P.S:
Have fun Lauren (and possibly Kelvy)!
Answer:
[tex]\displaystyle \frac{2 \cdot sin2x-cos2x}{5e^x} + C[/tex]
Step-by-step explanation:
The integration by parts formula is: [tex]\displaystyle \int udv = uv - \int vdu[/tex]
Let's find u, du, dv, and v for [tex]\displaystyle \int e^-^x \cdot cos2x \ dx[/tex] .
[tex]u=e^-^x[/tex][tex]du=-e^-^x dx[/tex] [tex]dv=cos2x \ dx[/tex] [tex]v= \frac{sin2x}{2}[/tex]Plug these values into the IBP formula:
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = e^-^x \cdot \frac{sin2x}{2} - \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex] [tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex]Now let's evaluate the integral [tex]\displaystyle \int \frac{sin2x}{2} \cdot -e^-^x dx[/tex].
Let's find u, du, dv, and v for this integral:
[tex]u=-e^-^x[/tex] [tex]du=e^-^x dx[/tex] [tex]dv=\frac{sin2x}{2} dx[/tex] [tex]v=\frac{-cos2x}{4}[/tex]Plug these values into the IBP formula:
[tex]\displaystyle \int -e^-^x \cdot \frac{sin2x}{x}dx = -e^-^x \cdot \frac{-cos2x}{4} - \int \frac{-cos2x}{4}\cdot e^-^x dx[/tex]Factor 1/4 out of the integral and we are left with the exact same integral from the question.
[tex]\displaystyle \int -e^-^x \cdot \frac{sin2x}{x}dx = -e^-^x \cdot \frac{-cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx[/tex]Let's substitute this back into the first IBP equation.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \Big [ -e^-^x \cdot \frac{-cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx \Big ][/tex]Simplify inside the brackets.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \Big [ \frac{e^-^x \cdot cos2x}{4} + \frac{1}{4} \int cos2x \cdot e^-^x dx \Big ][/tex]Distribute the negative sign into the parentheses.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4} - \frac{1}{4} \int cos2x \cdot e^-^x dx[/tex]Add the like term to the left side.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx + \frac{1}{4} \int cos2x \cdot e^-^x dx= \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4}[/tex] [tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{e^-^x sin2x}{2} - \frac{e^-^x \cdot cos2x}{4}[/tex]Make the fractions have common denominators.
[tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x}{4} - \frac{e^-^x \cdot cos2x}{4}[/tex]Simplify this equation.
[tex]\displaystyle \frac{5}{4} \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{4}[/tex]Multiply the right side by the reciprocal of 5/4.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{4} \cdot \frac{4}{5}[/tex]The 4's cancel out and we are left with:
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2e^-^x sin2x - e^-^x cos2x}{5}[/tex]Factor [tex]e^-^x[/tex] out of the numerator.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{e^-^x(2 \cdot sin2x-cos2x)}{5}[/tex]Simplify this by using exponential properties.
[tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2 \cdot sin2x-cos2x}{5e^x}[/tex]The final answer is [tex]\displaystyle \int e^-^x \cdot cos2x \ dx = \frac{2 \cdot sin2x-cos2x}{5e^x} + C[/tex].
Answer:
[tex]\displaystyle\int e^{-x}\cos(2x)\, dx=\frac{2\sin(2x)-\cos(2x)}{5e^x}+C[/tex]
Step-by-step explanation:
We would like to integrate the following integral:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx[/tex]
Since this is a product of two functions, we can consider using Integration by Parts given by:
[tex]\displaystyle \int u\, dv =uv-\int v\, du[/tex]
So, let’s choose our u and dv. We can choose u base on the following guidelines: LIATE; or, logarithmic, inverse trig., algebraic, trigonometric, and exponential.
Since trigonometric comes before exponential, we will let:
[tex]u=\cos(2x)\text{ and } dv=e^{-x}\, dx[/tex]
By finding the differential of the left and integrating the right, we acquire:
[tex]du=-2\sin(2x)\text{ and } v=-e^{-x}[/tex]
So, our integral becomes:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=(\cos(2x))(-e^{-x})-\int (-e^{-x})(-2\sin(2x))\, dx[/tex]
Simplify:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\int e^{-x}\sin(2x)\, dx[/tex]
Since we ended up with another integral of a product of two functions, we can apply integration by parts again. Using the above guidelines, we get that:
[tex]u=\sin(2x)\text{ and } dv=e^{-x}\, dx[/tex]
By finding the differential of the left and integrating the right, we acquire:
[tex]du=2\cos(2x)\, dx\text{ and } v=-e^{-x}[/tex]
This yields:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\Big[(\sin(2x))(-e^{-x})-\int (-e^{-x})(2\sin(2x))\, dx\Big][/tex]
Simplify:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)-2\Big[-e^{-x}\sin(2x)+2\int e^{-x}\cos(2x)\, dx\Big][/tex]
We can distribute:
[tex]\displaystyle \int e^{-x}\cdot \cos(2x)\, dx=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)-4\int e^{-x}\cos(2x)\, dx[/tex]
The integral on the right is the same as our original integral. So, we can isolate it:
[tex]\displaystyle \Big(\int e^{-x}\cos(2x)\, dx\Big)+4\Big(\int e^{-x}\cos(2x)\, dx)\Big)=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)[/tex]
Combine like integrals:
[tex]\displaystyle 5 \int e^{-x}\cos(2x)\, dx=-e^{-x}\cos(2x)+2e^{-x}\sin(2x)[/tex]
We can factor out an e⁻ˣ from the right:
[tex]\displaystyle 5\int e^{-x}\cos(2x)\, dx=e^{-x}\Big(-\cos(2x)+2\sin(2x)\Big)[/tex]
Dividing both sides by 5 yields:
[tex]\displaystyle \int e^{-x}\cos(2x)\, dx=\frac{e^{-x}}{5}\Big(-\cos(2x)+2\sin(2x)\Big)[/tex]
Rewrite. We of course also need the constant of integration. Therefore, our final answer is:
[tex]\displaystyle\int e^{-x}\cos(2x)\, dx=\frac{2\sin(2x)-\cos(2x)}{5e^x}+C[/tex]
A store is having a sale. All items for sale are discounted 15%. If the regular price of a bedspread is $45, what is the sale price?
(I NEED THIS QUICK)
Answer:
$38.25
Step-by-step explanation:
45 × 0.15 = 6.75
45 - 6.75 = 38.25
The sale price of the item will be $38.25
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that a store is having a sale. All items for sale are discounted by 15%. the regular price of a bedspread is $45,
The discounted price will be calculated as:-
45 × 0.15 = 6.75
45 - 6.75 = $38.25
Therefore, the sale price of the item will be $38.25
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Aaliyah is 3 times as old as AJ. 4 years ago, Aaliyah was 7 times as old as AJ. How old is Aaliyah now?
Answer:
Aaliyah is 18years old now
Step-by-step explanation:
let AJ's age=x
Aaliyah's age=3x
Four years ago,
AJ's age=x-4
Aaliyah's age=3x-4
3x-4=7(x-4)
3x-4=7x-28
3x-7x=-28+4
-4x=-24
x=6
Aaliyah's present age=3x=3×6=18