Answer:
{-12, 9, 24}
Step-by-step explanation:
Set the given f(x) = (x - 9)(x + 12)(x - 24) = to 0. Then, one by one, set each factor = to 0 and solve for x: We get the zeros {-12, 9, 24}
Answer: x = 9, x = −12, x = 24
What are the intercepts of the line
Answer:
y intercept (0,-32)
x intercept (3.2,0)
Step-by-step explanation:
To find the y intercept set x = 0 and solve for y
y = 10x -32
y = 0-32
y = -32
(0,-32)
To find the x intercept set y = 0 and solve for x
y = 10x -32
0 = 10x -32
Add 32 to each side
32 = 10x
Divide by 10
32/10 = x
(3.2,0)
Answer:
[tex]y-intercept(0,-32)\\\\x-intercept(\frac{16}{5},0)[/tex]
Step-by-step explanation:
The y-intercept happens where x is 0, and the x-intercept if where y is 0. You can use this knowledge to find the intercepts.
This equation is written in slope-intercept form:
[tex]y=mx+b[/tex]
where b is the y-intercept, so the y-intercept is -32.
To find the x intercept, insert 0 as the value of y:
[tex]0=10x-32[/tex]
Solve for x. Add 32 to both sides:
[tex]0+32=10x-32+32\\\\32=10x[/tex]
Divide both sides by 10:
[tex]\frac{32}{10}=\frac{10x}{10} \\\\x=\frac{32}{10} =\frac{16}{5}[/tex]
The x-intercept is at [tex]\frac{16}{5}[/tex] or [tex]3.2[/tex] .
Find the points:
[tex]y-intercept(0,-32)\\x-intercept(\frac{16}{5},0)[/tex]
Finito.
Over the last 4 years, Micheal has earned $240 interest on an initial investment of 2,000. What simple annual interest rate in the bank paying on this account?
Answer:
3% simple interest
Step-by-step explanation:
Simple interest formula is:
I = P*r*t
P = $2000
r = ?
t = 4
I = $240
240 = 2000 * r * 4
60 = 2000r
r = 60/2000
r = 3/100 = 0.03 = 3%
Select all that apply.
What types of triangles can have an obtuse angle?
scalene
isosceles
acute
right
Answer:
Isosceles and Scalene
Step-by-step explanation:
I did some research and plus we learned about angles and triangles in Geometry.
Plz click the Thanks button!
<Jayla>
Answer:
Isosceles and Scalene
Step-by-step explanation:
What’s the solution to #4?
Answer:
95/pie
Step-by-step explanation:
2 × radius = diameter
2 × pie × radius = circumference
2 × pie × radius = 95cm
radius = 95/2 × pie
Diameter = [95/2 × pie] × 2
Diameter = 190/2 × pie
Diameter = 95/pie
(It wasn't stated in the question but if pie = 22/7, the diameter is 95 × 7/22 = 30.23 (approximately)
A has coordinates (-2,-5) what is A' after a Dilation with a scale factor of N = -3.
Answer:
A' = (6, 15)
Step-by-step explanation:
We consider the center point of dilation to be the origin (0,0)
so point A(-2, -5) to A' by scale factor N = -3 means
A' = (-2*(-3), -5*(-3)) = (6, 15)
What is the value of x
Answer:
x=123
Step-by-step explanation:
x is across from the angle that measures 123 degrees. Therefore, they are vertical angles, and are congruent.
x=123
Additionally, 57 and x are on a straight line. This means they are supplementary and add to 180 degrees
57*x=180
Subtract 57 from both sides to get x by itself.
x=123
-7 2/3 +(5 1/2) + 8 3/4 =
Answer:
6 7/12
Step-by-step explanation:
-7 2/3 +(5 1/2) + 8 3/4
Get a common denominator of 12
-7 2/3 * 4/4 +(5 1/2 +6/6) + 8 3/4*3/3
-7 8/12 + 5 6/12 + 8 9/12
Subtract the first two terms first
They have opposite signs so subtract and take the sign of the larger
-7 8/12 + 5 6/12 = -2 2/12
-2 2/12 + 8 9/12
They have opposite signs so subtract and take the sign of the larger
-2 2/12 + 8 9/12 = 6 7/12
how many minutes is 504 hours
Answer:
30,240 minutes
Step-by-step explanation:
Hope this helps :)
30240 minutes for 504 hours
a sphere has surface area 16pi. find the radius
Answer:
2.
Step-by-step explanation:
Take the surface area and divide it by pi. Then take that value, and square root it. Then, divide by two. In this case, you get two.
The radius of a sphere with a surface area of 16pi is calculated using the formula for the surface area of a sphere, resulting in a radius of 2 units.
Explanation:To find the radius of a sphere with a surface area of 16π, you can use the formula for the surface area of a sphere which is surface area = 4 π (r)². By setting the surface area to 16π and solving for r, you have:
16π = 4πr²
Dividing both sides by 4π leaves you with r² = 4, and taking the square root of both sides gives you r = 2. Therefore, the radius of the sphere is 2 units.
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What are the intercepts of the function?
The x-intercepts are
The y-intercept is
Answer:
x intercepts: x=-1 and x=-11
y intercepts: y = 11
Step-by-step explanation:
x+1=0
x=-1
x+11=0
x=-11
f(0)=11
Answer:
x intercept is -1,0 and -11,0 and y intercept is 0,11
Step-by-step explanation:
i need help.....
due friday
Simply find the volume of each figure using their corresponding formulas and compare them! :D
CYLINDER: πr2h
CONE: πr2h ÷ 3
CYLINDER WORK:
Your radius is 2, which was a simple find! It wants it squared, so simply do 2x2 to get your squared radius of 4. Now that you know this, as well as your height, which is 3, let's plug it in!
π×4×3 (I would suggest putting this in your calculator)
=37.7
CONE WORK:
Your radius is 2 again, which was a simple find because its half your diameter, or 4! It wants it squared again, so simply do 2x2 to get your squared radius of 4. Now that you know this, as well as your height, which is 9, let's plug it in! The only difference is you have to divide your whole answer by three since it's different for a cone.
π×4× 9 ÷ 3 (I would suggest putting this in your calculator)
=37.7
Well, what a coincidence, they are the same! This proves that it does not depend on the height, it will only depend on the proportions of your shape, since the cylinder could have had a much larger scale of numbers, which would make it bigger not based on it's shape, but it's overall size.
Alexander is a stockbroker. He earns 13% commission each week. Last week, he sold $4 comma 500 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011?
Multiply the amount he sold by the percent of commission:
4500 x 0.13 = 585
he made $585 last week.
There are 52 weeks in a year, multiply the amount of commission by 52:
585 x 52 = 30,420
he made $30,420 in 2011.
Alexander made $585 in commission last week. In 2011, he made $30,420 in commission.
Explanation:To calculate Alexander's commission, we can multiply the value of the stocks he sold by the commission rate.
$4,500 imes 0.13 = $585
Therefore, Alexander made $585 in commission last week.
To calculate how much he made in commission in 2011, we need to know the number of weeks in 2011. Assuming there are 52 weeks in a year, we can multiply Alexander's weekly commission by the number of weeks in 2011:
$585 imes 52 = $30,420
PLEASE HELP ME! I ONLY HAVE 2 HOURS!!!
What is the sample space for choosing 1 jelly bean at random from a jar containing 5 red, 7 blue, and 2 green jelly beans?
A. {5, 7, 2}
B. {red, blue, green}
C. {5 red, 7 blue, 2 green}
D. {red, blue, orange}
Answer:
B. red, blue, green
Using the sample space concept, it is found that for this situation, it is given by:
B. {red, blue, green}
------------------------
In a probability experiment, the sample space is the set that contains all possible outcomes.For example, if you are going to have a child, it will either be a boy or a girl, thus, the sample space is: {boy, girl}In this question, one jelly bean will be chosen, which will either be red, blue or green. Thus, the possible outcomes are red, blue or green, which means that the sample space is: {red, blue, green}, given by option B.A similar problem is given at https://brainly.com/question/15006554
A flagpole is at a (3x + 24)degrees° angle from the ground. Find the value of x.
The value of x is 22. The angle the flagpole makes with the ground, represented as 3x+24∘, is supplementary to the angle the flagpole makes with the vertical line, which is 90 degrees. By setting up the equation 3x+24° + 90° =180°. and solving for x, we find =22. Thus, the flagpole makes a 3(22) + 24° + 90° =180° angle with the ground.
Certainly, let's break it down step by step:
Given: The angle the flagpole makes with the ground is [tex]\(3x + 24^\circ\).[/tex]
1. **Define the problem**: Let [tex]\( \theta \)[/tex] represent the angle the flagpole makes with the ground.
2. **Write the given information**:
[tex]\[ \theta = 3x + 24^\circ \][/tex]
3. **Understand the geometric situation**: The angle formed by the flagpole with the ground is supplementary to the angle formed by the flagpole with the vertical line
4. **Write the equation based on the supplementary angles relationship**:
[tex]\[ \theta + 90^\circ = 180^\circ \][/tex]
5. **Substitute the given value of [tex]\( \theta \)[/tex]**:
[tex]\[ (3x + 24^\circ) + 90^\circ = 180^\circ \][/tex]
6. **Simplify the equation**:
[tex]\[ 3x + 24^\circ + 90^\circ = 180^\circ \][/tex]
7. **Combine like terms**:
[tex]\[ 3x + 114^\circ = 180^\circ \][/tex]
8. **Isolate \(x\)**:
[tex]\[ 3x = 180^\circ - 114^\circ \][/tex]
[tex]\[ 3x = 66^\circ \][/tex]
[tex]\[ x = \frac{66^\circ}{3} \][/tex]
[tex]\[ x = 22 \][/tex]
[tex]So, \( x = 22 \).[/tex]
Which expression represents the greatest common factor (GCF) of 16 and 40? A. 2 x 2 B. 2 x 2 x 3 C. 2 x 2 x 5 D. 2 x 2 x 2
someone plz help me
Answer:
D. 2 x 2 x 2
Step-by-step explanation:
16 is: 2 x 2 x 2 x 2
40 is: 2 x 2 x 2 x 5
16 and 40 have in common are: 2 x 2 x 2
What is the volume of the cylinder below?
O A. 45 pi units
OB. 72 pi units
O C. 90 pi units
O D. 36 pi units
Answer D.36 pi unit 3
Answer:
36
Step-by-step explanation:
appeex
The line of best fit for the scatterplot below passes through which pair of points?
A. P and Q
B. P and T
C. R and Q
D. S and Q
Answer:
C. R and Q
Step-by-step explanation:
If you draw the line of best fit, it passes through the cluster of points along the graph. The two points that are included in the mass are R and Q. The other ones are outliers, and would not be represented on the line of best fit.
I hope this helps!
Answer:
R and Q
Step-by-step explanation:
e.dgenuity
A scatterplot is used to display data where x is the amount of time, in minutes, one member can tolerate the heat in a sauna, and
y is the temperature, in degrees Fahrenheit, of the sauna.
Which interpretation describes a line of best fit of y = -1.5x + 173 for the data?
Answer: A the member can tolerate a temp of 173 fahrenheit for 0 minutes
The true statement is (a) The member can tolerate a temperature of 173∘ Fahrenheit for 0 minutes.
How to interpret the line of best fit?The equation of the line of best fit for the data is given as:
y = -1.5x + 173
Set x to 0, to calculate the y-intercept
y = -1.5 * 0 + 173
Evaluate the product
y = 0 + 173
Evaluate the sum
y = 173
This means that initial temperature is 173
Hence, the true statement is (a) The member can tolerate a temperature of 173∘ Fahrenheit for 0 minutes.
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The sum of three consecutive numbers is 72. What is the smallest of
these numbers?
x + (x + 1) + (x + 2) = 72
x+ (x + 2) + (x + 4) = 72
3x = 72
x + y + z =72
Answer:
The smallest number is 23
Step-by-step explanation:
Let x be the first number
x+1 is the next consecutive number
x+2 is the next consecutive number
The sum is
x+ x+1 + x+2 = 72
Combine like terms
3x+3 = 72
subtract 3 from each side
3x+3-3 = 72-3
3x = 69
Divide each side by 3
3x/3 = 69/3
x = 23
x+1 = 24
x+2 =25
The numbers are
23,24,25
Find the median of each set of data.
12, 8, 6, 4, 10, 1
6,3, 5, 11,2, 9,5, 0
30, 16, 49, 25
What is the volume of a cylinder with base radius 2 and height 6?
Answer:
24π cubic units
Step-by-step explanation:
Using the formula for the volume of a cylinder, you find it to be ...
V = πr²h
V = π(2²)(6)
V = 24π . . . . cubic units
PLEASE HELP I need an explanation if you can’t do it it’s fine I’ll take what I can get thanks!
Answer: A. 169.65 mi^3
Step-by-step explanation:
The volume of a cylinder is formula is v= π *r^2 *h where r is radius and h is the height being multiplied pie.
V= 3.14 * 3^2 * 6
v= 3.14 * 9 * 6
v =169.6460 to the nearest hundredth is 169.65
factor the trinomial PLEASE HURRY! 2x
2
+11x+12
Answer:
2
x
,
2
,
11
x
+
12
2x,2,11x+12
Hope this helpsAnswer:
0
Step-by-step explanation:
What are the x-intercepts of the function f(x) = –2x2 – 3x + 20? (–4, 0) and five-halves five-halves and (4, 0) (–5, 0) and (2, 0) (–2, 0) and (5, 0)
Answer:
(-4, 0) and (5/2, 0)
Step-by-step explanation:
f(x) = –2x2 – 3x + 20
factor using the diamond method
-2*20 = -40
so -8 * 5 = -40 and -8 + 5 = -3 so...
f(x) = -2x^2 - 8x + 5x + 20
f(x) = -2x (x + 4) + 5 *(x + 4)
f(x) = (-2x + 5)*(x + 4)
x-intercepts are x = 5/2 and x =-4
(-4, 0) and (5/2, 0)
Answer:
(-4, 0) and (5/2, 0)
Step-by-step explanation:
help me please!!!!! what is the answer?????
Answer:
The answer will be number 3
8.917
Answer:
i think 3
Step-by-step explanation:
Can someone please help me with this?
Answer:
a
Step-by-step explanation:
for x<2, the slope is negative and y-intercept is 3.5
for x>=2, slope is positive and y-intercept is 4
only a satisfies the condition
A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the 0.10 significance level, is there a difference in the population means?
(a) state the decision rule
(b) compute the pooled estimate of the population variance
(c) compute the test statistic
(d) state your decision about the null hypothesis
(e) estimate the p-value.
Answer:
a) [tex] df =n_1 +n_2 -2 =15 +17-2 =30[/tex]
And then since we want to conduct a two tailed test we need to llok in the t distribution with 30 degrees of freedom a value who accumulate 0.05 of the area and we got:
[tex] t_{\alpha/2} =\pm 1.697[/tex]
b)[tex]S^2_p =\frac{(15-1)(12)^2 +(17 -1)(15)^2}{15 +17 -2}=187.2[/tex]
[tex]S_p=13.682[/tex]
c) [tex]t=\frac{(350 -342)-(0)}{13.682\sqrt{\frac{1}{15}+\frac{1}{17}}}=1.65[/tex]
d) For this case the statistic calculated is lower than the critical value so then we FAIL to reject the null hypothesis at the significance level given.
e) The p value for this case would be given by:
[tex]p_v =2*P(t_{30}>1.65) =0.1094[/tex]
Step-by-step explanation:
We are assuming that the two population deviations are equal:
[tex]\sigma^2_1 =\sigma^2_2 =\sigma^2[/tex]
And the statistic is given by this formula:
[tex]t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}[/tex]
Where t follows a t distribution with [tex]n_1+n_2 -2[/tex] degrees of freedom and the pooled variance [tex]S^2_p[/tex] is given by this formula:
[tex]\S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}[/tex]
Part a
For this case we need to find the degrees of freedom given by:
[tex] df =n_1 +n_2 -2 =15 +17-2 =30[/tex]
And then since we want to conduct a two tailed test we need to llok in the t distribution with 30 degrees of freedom a value who accumulate 0.05 of the area and we got:
[tex] t_{\alpha/2} =\pm 1.697[/tex]
Part b
The pooled deviation can be founded with this formula:
[tex]S^2_p =\frac{(15-1)(12)^2 +(17 -1)(15)^2}{15 +17 -2}=187.2[/tex]
And the deviation would be:
[tex]S_p=13.682[/tex]
Part c
The system of hypothesis on this case are:
Null hypothesis: [tex]\mu_1 = \mu_2[/tex]
Alternative hypothesis: [tex]\mu_1 \neq \mu_2[/tex]
Replacing the info given we got:
[tex]t=\frac{(350 -342)-(0)}{13.682\sqrt{\frac{1}{15}+\frac{1}{17}}}=1.65[/tex]
Part d
For this case the statistic calculated is lower than the critical value so then we FAIL to reject the null hypothesis at the significance level given.
Part e
The p value for this case would be given by:
[tex]p_v =2*P(t_{30}>1.65) =0.1094[/tex]
The question refers to hypothesis testing for difference in population means. The null hypothesis is rejected both by using the critical value approach and the p-value approach, indicating a significant difference in population means at the 0.10 significance level.
Explanation:This question deals with hypothesis testing for difference in population means with a given significance level.
(a) The decision rule for this two-tailed test is: Reject the null hypothesis if the absolute value of the test statistic is greater than the critical value at the 0.10 significance level, or if the p-value is less than the significance level.
(b) The pooled estimate of the population variance is calculated using the formula: [(n1-1)s1^2 + (n2-1)s2^2] / (n1+n2-2) = [(15-1)*12^2 + (17-1)*15^2] / (15+17-2) = 196.77.
(c) The test statistic is calculated as: (x1 - x2) / sqrt[(pooled variance)*(1/n1 + 1/n2)] = (350 - 342) / sqrt[(196.77)*(1/15 + 1/17)] = 1.87.
(d) With degrees of freedom of (15+17-2)=30, the critical values for a two-tailed test at the 0.10 significance level are approximately ±1.697. As our test statistic is greater than the critical value, we reject the null hypothesis.
(e) The p-value associated with the test statistic of 1.87 is approximately 0.07, which is less than the significance level of 0.10. Hence, we again reject the null hypothesis. Therefore, we conclude that there is a significant difference in the population means at the 0.10 significance level.
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How many solutions does this equation have?
15x -5
no solution
exactly one solution
exactly two solutions
infinitely many solutions
Answer: Infinite solutions.
x could be equal to anything, and you can't solve for x since there is no equation on the other side of an equal sign for you to solve it. Hope that helps.
The answer is A on USA test prep
Step-by-step explanation:
Which exponential equation best models the data
in the graph?
y = 0.85(25)Oy=0.85(25)5x
y=25(0.8.A) y = 25(0,85)5x
Answer C
Answer:
C
Step-by-step explanation:
The solution is: quadratic; y = 2.5x^2, this function best models the data.
Option (1)
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
given that,
x -2 -1 0 1 2
y 10 2.5 0 2.5 3.0
Ist difference,
d_1 = -7.5
d_2= -2.5
d_3 = 2.5
d_4 = 7.5
2nd difference,
x_1 = 5
x_2 = 5
x_3 = 5
Since 2nd difference is common, given table represents a quadratic equation.
Let the equation is,
y = ax²+ bx + c
For a point (0, 0) passing through the quadratic equation,
0 = c
Therefore, quadratic equation is y = ax² + bx
Since ordered pair (-1, 2.5) passes through the graph of the function,
2.5 = a(-1)² + b(-1)
a - b = 2.5 ------(1)
For another point (1, 2.5)
2.5 = a(1)² + b(1)
a + b = 2.5 ------(2)
By adding equations (1) and (2),
2a = 5
a = 2.5
and from equation (2)→ y = 0
Therefore, equation of the quadratic function given in the table is y = 2.5x²
Option (1) is the answer.
Hence, The solution is: quadratic; y = 2.5x^2, this function best models the data. i.e. Option (1)
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Complete question:
Graph the data in the table. Which kind of function best models the data? Write an equation to model the data. quadratic; y = 2.5x2 linear; y = 2.5x quadratic; y = –2.5x2 exponential; y = 2.5x
The perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensionsThe perimeter of the rectangle is 44. the length is five less than double the width. find the dimensions
Answer:
Length = 13
Width = 9
Step-by-step explanation:
The equation to find the perimeter is 2l+2w=44. The second equation is 2w-5=l since the length is 5 less than double the width.
2l+2w=44,2w-5=l (write equations)
use the equation for length, the second equation, and subtitute it into the first equation's l. Since all l is the same and 2w-5 is equal to l, we can use that equation for the l in 2l+2w=p
2(2w-5)+2w=44 (subtitute)
4w-10+2w=44
6w-10=44 (simplify)
6w=54 (add 10 to both sides)
w=9
use the width to find the length by plugging it into any original equation
2w-5=l
2(9)-5=l
18-5=l
13=l
Answer:
The length is 13.
The width is 9.
Step-by-step explanation:
length = x
width = w
1) x = 2w - 5
2) 44 = 2x + 2w
3) 44 = 2(2w - 5) + 2w
4) 44 = 4w - 10 + 2w
5) 44 = 6w - 10
6) 54 = 6w
7) w = 9
8) x = 2(9) - 5
9) x = 18 - 5
10) x = 13