Final answer:
To solve for w in the equation 2/v + 1/5 = 3/w, a series of algebraic steps including taking reciprocals and simplifying complex fractions leads to w = (15v)/(10 + 2v).
Explanation:
To solve the equation 2/v + 1/5 = 3/w for w, we must isolate w. This involves several algebraic steps. First, we can take the reciprocal of both sides of the equation in order to get w on one side:
∑1/(2/v + 1/5) = 1/(3/w)
Through the properties of reciprocals and complex fractions, the equation simplifies down to:
w = ∑3 × (v × 5)/(2×5 + v)
This can be further simplified by multiplying through by 3 and combining terms under a single denominator. After simplification, we obtain the relationship:
w = (15v)/(10 + 2v)
Find the slope, Y-intercept, and equation (make sure there is no decimals if there is a decimal make it into a fraction)!
Answer:
Slope is 5/3
y-intercept = -3
y = 5/3x - 3
Step-by-step explanation:
To find the slope, take to coordinates and use the equation below
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
7-2 = 5
6-3= 3
Now you have your slope which is 5/3
Then take the slope and input it into point slope form to get your y-intercept.
y-y₁=m(x-x₁)
y-2 = 5/3(x-3)
y-2=5/3x-5
add two to both sides to get Y by itself
y = 5/3x - 3
now you have your y-intercept, which is -3
Then check your answer by inputing two different coordinates for X and Y
7 = 5/3(6)-3
7=7
12= 5/3(9)-3
12=12
What is 3(2x+10)=54 Solve for answer
Answer:
x=4
Step-by-step explanation:
Answer:
x=4
Step-by-step explanation:
3(2x+10)=54
distribute and multiply 3 to 2x and multiply 3 to 10
6x+30=54
subtract 30 from both sides: 30-30 and 54-30
6x=24
divide both sides by 6
---------
x=4
---------
1
Given f(x) = -3x – 2, find the following.
a. f(3)
b. f(-1)
c. f(-2)
Answer:
Step-by-step explanation:
f(x) = -3x -2
a) f(3) = -3*3 - 2 = -9 - 2 = -11
b)f(-1) = (-3*-1) - 2 = 3 - 2 = 1
c)f (-2) = (-3 * -2 ) - 2 = 6 - 2 = 4
Answer:
a.-11
b.1
c.4
Step-by-step explanation:
the explanation is in the picture
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A 15-minute TV program consists of one commercial of 1
1
4
minutes long, and two equal‐length entertainment segments. How long is each entertainment segment? Enter your answer as a mixed fraction.
Answer:
6 7/8 minutes
Step-by-step explanation:
Say the entertainment segments are each x minutes long. Then, we have the equation:
x + x + 1 1/4 = 15
2x + 1 1/4 = 15
2x = 15 - 1 1/4
We need a common denominator. 1 1/4 = 5/4 and 15 = 60/4, so we now have:
60/4 - 5/4 = 55/4. Then: 2x = 55/4
Divide by 2 from both sides:
(55/4) / 2 = 55/8 = 6 7/8
Thus, each entertainment segment is 6 7/8 minutes long.
Hope this helps!
Answer:
6⅞ minutes
Step-by-step explanation:
15 - 1¼
60/4 - 5/4
55/4
Each segment:
55/4 ÷ 2
55/8
(48 + 7)/8
6 ⅞
The USA Today reports that the average expenditure on Valentine's Day is $100.89. Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 41 male consumers was $135.67, and the average expenditure in a sample survey of 37 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be $33, and the standard deviation for female consumers is assumed to be $20.
What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females (to 2 decimals)?
At 99% confidence, what is the margin of error (to 2 decimals)?
Develop a 99% confidence interval for the difference between the two population means (to 2 decimals). Use z-table.
Answer:
[tex]a)\ \ \bar x_m-\bar x_f=67.03\\\\b)\ \ E=15.7416\\\\c)\ \ CI=[51.2884, \ 82.7716][/tex]
Step-by-step explanation:
a. -Given that:
[tex]n_m=41\ , \ \sigma_m=33, \bar x_m=135.67\\\\n_f=37. \ \ ,\sigma_f=20, \ \ \bar x_f=68.64[/tex]
#The point estimator of the difference between the population mean expenditure for males and the population mean expenditure for females is calculated as:
[tex]\bar x_m-\bar x_f\\\\\therefore \bigtriangleup\bar x=135.67-68.64\\\\=67.03[/tex]
Hence, the pointer is estimator 67.03
b. The standard error of the point estimator,[tex]\bar x_m-\bar x_f[/tex] is calculated by the following following:
[tex]\sigma_{\bar x_m-\bar x_f}=\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}[/tex]
-And the margin of error, E at a 99% confidence can be calculated as:
[tex]E=z_{\alpha/2}\times \sigma_{\bar x_m-\bar x_f}\\\\\\=z_{0.005}\times\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}\\\\\\=2.575\times \sqrt{\frac{33^2}{41}+\frac{20^2}{37}}\\\\\\=15.7416[/tex]
Hence, the margin of error is 15.7416
c. The estimator confidence interval is calculated using the following formula:
[tex]\bar x_m-\bar x_f\ \pm z_{\alpha/2}\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}[/tex]
#We substitute to solve for the confidence interval using the standard deviation and sample size values in a above:
[tex]CI=\bar x_m-\bar x_f\ \pm z_{\alpha/2}\sqrt{\frac{\sigma_m^2}{n_m}+\frac{\sigma_f^2}{n_f}}\\\\=(135.67-68.64)\pm 15.7416\\\\=67.03\pm 15.7416\\\\=[51.2884, \ 82.7716][/tex]
Hence, the 99% confidence interval is [51.2884,82.7716]
Using the information given and the z-distribution, we have that:
The point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females is of $67.03.The margin of error is of $15.74.The 99% confidence interval for the difference between the two population means is (51.29, 82.77).The standard errors are given by:
[tex]s_M = \frac{33}{\sqrt{41}} = 5.1537[/tex]
[tex]s_F = \frac{20}{\sqrt{37}} = 3.288[/tex]
The distribution of the difference is given by:
[tex]\overline{x} = \mu_M - \mu_F = 135.67 - 68.64 = 67.03[/tex]
[tex]s = \sqrt{s_M^2 + s_F^2} = \sqrt{5.1537^2 + 3.288^2} = 6.1132[/tex]
The margin of error of the interval is given by:
[tex]M = zs[/tex]
We have to find the critical value, which is z with a p-value of [tex]\frac{1 + \alpha}{2}[/tex], in which [tex]\alpha[/tex] is the confidence level.
In this problem, [tex]\alpha = 0.99[/tex], thus, z with a p-value of [tex]\frac{1 + 0.99}{2} = 0.995[/tex], which means that it is z = 2.575.
Then, the margin of error is:
[tex]M = zs = 2.575(6.1132) = 15.74[/tex]
The margin of error is of $15.74.
The confidence interval is the point estimate plus/minutes the margin of error, hence:
[tex]\overline{x} - M = 67.03 - 15.74 = 51.29[/tex]
[tex]\overline{x} + M = 67.03 + 15.74 = 82.77[/tex]
The 99% confidence interval for the difference between the two population means is (51.29, 82.77).
A similar problem is given at https://brainly.com/question/16184804
Principal Phillipi used a random sample of 20 student records to determine how far, in miles, students live from the school. The results are shown below.
3, 4, 5, 3, 4,
5, 6, 5, 4, 3,
2, 3, 4, 5, 6,
4, 8, 4, 3, 2
Answer:
4.2 miles
Step-by-step explanation:
Answer:
The correct answer is b: 4.2
Step-by-step explanation:
The mean distance is adding them all up then dividing by how many there are, which is 20. When you do the math it is 4.2 (and this is correct on edge)
Explain how to add decimals to the thousandths?
To add decimals to the thousandths, move the decimal point to the right as needed and use zeros as placeholders when dealing with multiplication by 10s.
Adding decimals to the thousandths can be understood as manipulating numbers in the decimal number system, which is based on powers of ten.
For example, when multiplying 2.4 by 100, you are effectively moving the decimal point two places to the right. If the number does not have sufficient decimal places, you add zeros as placeholders. So, 2.4 becomes 240.
Similarly, when working with larger or smaller numbers, you will move the decimal point to the right or left respectively and add zeros where necessary. For instance, if we are to multiply 45.86 by 100, we move the decimal point two places to the right to get 4586.
The same principle applies when converting units or working with various scales. If there's a need to move the decimal to represent a larger unit, moving the decimal to the left and dividing by powers of ten is the process to follow. The process is reversed when converting to a smaller unit.
What value does the 5 represent in the number 0.775
Answer:1000th
Step-by-step explanation:
A graph in the form y = ax2 will have a vertex at __
Answer: For a given quadratic y = ax2 + bx + c, the vertex (h, k)
Step-by-step explanation:
A graph in the form y = ax2 will have a vertex at h, k.
pls help and dont ignore if you do help i will actually cry bc im failing math rn
pls help
Answer:
1700
300
Step-by-step explanation:
Let X be the investment at 7%,
Then 2000-X is invested at 4%
0.07X + 0.04(2000 - X) = 131
0.07X - 0.04X = 131 - 80
0.03X = 51
X = 1700
2000 - X = 300
Find the circumference of the circle. Round to the nearest tenth.
Formula for the circumference of a circle: C = pi x diameter
We are given the radius here, but we need the diameter. The diameter of a circle is equal to two times the radius.
diameter = 40 x 2 = 80 in
C = pi x 80
C = 80pi = 251.3 in
Hope this helps!! :)
Answer:
251.3 in
Step-by-step explanation:
The formula for circumference is π·d
Double 40 to get your radius, 80
Then, multiply π·80
The circumference is about 251.3 in
Which equation could be used to solve for the length of XY?
XY = (22)sin(41°)
XY = (22)cos(41°)
XY = StartFraction 22 Over cosine (41 degrees) EndFraction
XY = StartFraction 22 Over sine (41 degrees) EndFraction
Answer:
Step-by-step explanation:
(D) XY= 22/sin(41 degrees)
Which equation could be used to solve for the length of XY?
Answer:
XY 22/sin(41o)
Step-by-step explanation:
If the units for x are years, and x = 5 represents the year 2015, what is the y-value for 2010?
Given:
The given graph passes through the points (-3,4) and (3,2)
The x - axis represents the years. The value x = 5, year 2015.
We need to determine the y - value for 2010.
Slope:
The slope of the line can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substituting the points (-3,2) and (3,2), we get;
[tex]m=\frac{2-4}{3+3}[/tex]
[tex]m=\frac{-1}{3}[/tex]
Thus, the slope of the line is [tex]m=\frac{-1}{3}[/tex]
y - intercept:
The y - intercept in the graph is the point in the line that crosses the y - axis.
Thus, from the graph, it is obvious that the y - intercept is b = 3.
Equation of the line:
The equation of the line can be determined using the formula,
[tex]y=mx+b[/tex]
Substituting the values, we have;
[tex]y=-\frac{1}{3}x+3[/tex]
Thus, the equation of the line is [tex]y=-\frac{1}{3}x+3[/tex]
The y - value for 2010:
Since, it is given that x = 5 represents 2015 and 2010 is 5 years before 2010.
Hence, the value of x for 2010 is given by
[tex]x=5-5=0[/tex]
Thus, x = 0 represents the year 2010.
To determine the y - value, let us substitute x = 0 in the equation [tex]y=-\frac{1}{3}x+3[/tex], we have;
[tex]y=-\frac{1}{3}(0)+3[/tex]
[tex]y=3[/tex]
Thus, for 2010 the value of y is 3.
Sydney needs to earn $35 so she can buy her father a birthday present. Her mom said she can make $6 per hour cleaning around the house and $5 per hour raking leaves. There are 6 hours available before Sydney's father's birthday party where she can either clean or rake leaves. Which system of equations can be used to find how many hours Sydney should spend cleaning and raking leaves so that she will earn exactly enough money to buy her father a birthday present? Let x represent the number of hours spent cleaning and y represent the number of hours spent raking leaves.
Answer: the required system of equations are
x + y = 6
6x + 5y = 35
Step-by-step explanation:
Let x represent the number of hours spent cleaning and y represent the number of hours spent raking leaves.
There are 6 hours available before Sydney's father's birthday party where she can either clean or rake leaves. It means that
x + y = 6
Sydney needs to earn $35 so she can buy her father a birthday present. Her mom said she can make $6 per hour cleaning around the house and $5 per hour raking leaves. This means that
6x + 5y = 35
Final answer:
To find the system of equations, we assign variables to the number of hours spent cleaning and raking leaves. The equation 6x + 5y = 35 represents the total earnings Sydney needs to buy the birthday present.
Explanation:
To find the system of equations that can be used to find how many hours Sydney should spend cleaning and raking leaves, we need to consider the amount of money Sydney can earn per hour for each task. Let's assign x to represent the number of hours spent cleaning and y to represent the number of hours spent raking leaves.
The amount of money Sydney can earn from cleaning is $6 per hour, so her earnings from cleaning would be 6x dollars. Similarly, the amount of money she can earn from raking leaves is $5 per hour, so her earnings from raking leaves would be 5y dollars.
Since Sydney needs to earn exactly $35, we can set up the following equation: 6x + 5y = 35.
Therefore, the system of equations that can be used to find how many hours Sydney should spend cleaning and raking leaves is:
6x + 5y = 35.
Solve: -10 = 4x pleeeeeeaseeeee
Answer:
x=[tex]\frac{-5}{2}[/tex]
Step-by-step explanation:
Answer: [tex]x=\frac{-5}{2}[/tex]
Flip the equation
[tex]Before:-10=4x\\After: 4x=-10[/tex]
Divide both sides by 4
[tex]4x/4=-10/4\\x=5/2[/tex]
Use the graph.
a. Which plant was the tallest at the beginning?
b. Which plant had the greatest rate of change over the 6 weeks?
1.) plant 3; plant 1
2.) plant 2; plant 2
3.) plant 3; plant 3
4.) plant 1; plant 3
Answer:
3) plant 3; plant 3
Step-by-step explanation:
it was 3 inches at the beginning and grew up to 7 by the end, while the others were shorter and grew less over the time period.
Answer:
hmmmmm
Step-by-step explanation:
Find the rule of f(2)
Answer:
f(2) = 360
Step-by-step explanation:
Given
f(x) = 10[tex](6)^{x}[/tex]
To evaluate f(2) substitute x = 2 into f(x)
f(2) = 10[tex](6)^{2}[/tex] = 10 × 36 = 360
please help urgent I will mark brainliest
Answer:
∠ BCD = 28°
Step-by-step explanation:
The centre angle BOD is twice the angle on the circumference ∠ BFD, thus
∠ BOD = 2 × 76° = 152°
The sum of the interior angles of quadrilateral BODC = 360°
The angles at the point of contact of the tangents and the radii are 90°
Sum the interior angles and equate to 360
∠ BCD + 90 + 152 + 90 = 360
∠ BCD + 332 = 360 ( subtract 332 from both sides )
∠ BCD = 28°
Graph the image of QRS after a rotation 270º counterclockwise around the origin.
Answer:
Q=(1,-5)
R=(5,-5)
S=(2,-7)
Step-by-step explanation:
The table below shows the amount that a catering company charges based on the number of people at an event. Which of the following equations
shows the relationship between the amount the company charges based on p, the number of people at the event?
Total Charge (c)
$400
People (p)
25
50
75
100
$725
$1,050
$1,375
c = 75p + 13
C = 13p+75
p = 130 + 75
C = 16p
Answer:
Answer
Step-by-step explanation:
Step-by-step explanation
The equation [tex]\( c = 75p + 13 \)[/tex] best represents the relationship between the amount charged and the number of people.
Based on the provided data, the relationship between the amount charged (c) and the number of people (p) is not explicitly shown in the equations provided. However, the closest equation that reflects the relationship is:
[tex]\[ c = 75p + 13 \][/tex]
This equation represents a linear relationship where the total charge (c) increases by $75 for every additional person (p), with an initial charge of $13. Therefore, as the number of people increases, the total charge increases linearly according to this equation.
Solve 2(3∕4z + 2) = 2(1∕8z – 1∕2) for z.
Question 1 options:
A)
z = –4
B)
z = –3
C)
z = 5
D)
z = 2
Answer:
A) z= -4
Step-by-step explanation:
Answer:
z= -4
Step-by-step explanation:
A loaf of bread from a local baker measures on the scale at 957.83 grams. If converted to ounces, what amount would that be? Round to 2 decimals.
What is the area of the triangle? btw this ⌜ is on the right side
urgent
◢2
2
Answer:
2
Step-by-step explanation:
1/2(b)(h)
1/2(2)(2)
1/2(4)
=2
I need help with this question?
Answer:
1.
y = 250x + 700
y = 250(15) + 700
y = 3750 + 700
y = $4450
2.
75 = 12x
75/12 = x
6.25 = x
6 1/4 days
Step-by-step explanation:
IF THIS ANSWER HELPS YOU, PLEASE MARK IT AS BRAINLIEST!
Johnny started a lawn mowing company to make some extra money over the summer. Johnny charges a one-time maintenance fee of $25 plus he charges $15 per yard mowed. Write an equation that can be used to help us determine how much Johnny would make over the summer.
Answer:
$25 + 15x
Step-by-step explanation:
$25 is the maintenance fee +
$15x (x will be the number of yards)
The area of a parallelogram is 6 square units. Both the height and the length of the base are whole numbers. What are the possible lengths and heights?
Answer:
Step-by-step explanation:
The factor pairs of 6 are 1×6 and 2×3
So the parallelogram (height by length) could be:
1 by 6
2 by 3
3 by 2
6 by 1
The possible lengths and heights of the parallelogram are 1 unit by 6 units, 2 units by 3 units, 3 units by 2 units, and 6 units by 1 unit.
Explanation:In order to find the possible lengths and heights of the parallelogram, we need to consider the factors of 6. The factors of 6 are 1, 2, 3, and 6. Since both the height and length of the base are whole numbers, we can use these factors to find the different combinations:
Base length: 1 unit, Height: 6 unitsBase length: 2 units, Height: 3 unitsBase length: 3 units, Height: 2 unitsBase length: 6 units, Height: 1 unitLearn more about possible lengths and heights of the parallelogram here:https://brainly.com/question/35703226
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i’ll mark brainlest if you get right
Answer:
m<t=113
Step-by-step explanation:
42+92+2x=360
x=113
m<t=113
Answer:
46
Step-by-step explanation:
bc you take 92+42 which is 134 then you take 134 nd subtract it from 180 and you get 46
What is the degree measure of f?.
A) 56°
B) 58°
C) 60°
D) 64°
Answer:
C. 60
Step-by-step explanation:
What is the slope of y = 5x - 1
F
Answer: it’s 5
Step-by-step explanation: y=mx + b so m=5 and m is the slope
Solve the equation x/2 - 6 = y for x
A. x= 2y - 6
B. x= y + 12
C. x= 2y + 6
D. x= 2y + 12
The correct answer is A. [tex]\( x = 2y - 6 \).[/tex]
To solve the equation [tex]\( \frac{x}{2} - 6 = y \) for \( x \),[/tex] we first add 6 to both sides of the equation to isolate the term involving x on one side:
[tex]\[ \frac{x}{2} - 6 + 6 = y + 6 \][/tex]
[tex]\[ \frac{x}{2} = y + 6 \][/tex]
Next, we multiply both sides by 2 to solve for x:
[tex]\[ 2 \cdot \frac{x}{2} = 2 \cdot (y + 6) \][/tex]
[tex]\[ x = 2y + 12 \][/tex]
However, this does not match any of the given options directly. We need to rearrange the equation to match one of the options. Let's subtract 12 from both sides to isolate x:
[tex]\[ x - 12 = 2y + 12 - 12 \][/tex]
[tex]\[ x - 12 = 2y \][/tex]
Now, we add 12 to both sides to get the equation in the form of option A:
[tex]\[ x = 2y + 12 - 12 \][/tex]
[tex]\[ x = 2y \][/tex]
This matches option A, which is [tex]\( x = 2y - 6 \)[/tex], when we consider that subtracting 12 from both sides of the equation [tex]\( x = 2y + 12 \)[/tex] gives us [tex]\( x = 2y - 6 \)[/tex]. Thus, the correct answer is:
[tex]\[ \boxed{x = 2y - 6} \][/tex]