Answer:
Step-by-step explanation:
Using the following data:
H0:p=0.40 (null hypothesis)
Ha:p>0.40 (alternative hypothesis)
The p-value was determined to be 0.001.
a significance level of 5%
Since the p value (0.001) is less than the significance level (0.05), we will reject the null hypothesis and then we would conclude that the proportion of students that are nursing majors is greater than 0.4.
Answer:
p value= 0.131
Step-by-step explanation:
Since we have calculated the test statistic, we can now proceed to find the p-value for this hypothesis test.Using the test statistic and since the hypothesis test is a left tailed test, the p-value will then be the area under the standard normal curve to the left of the test statistic of -1.12.Using the Standard Normal table given above, the area under the standard normal curve to the left of the test statistic of -1.12 is 0.131 (rounded to 3 decimal places.Thus the p-value = 0.131.
I made a square frame for my favorite bird picture from four wooden pieces. Each piece is a rectangle with a perimeter of 24 inches. What is the area and perimeter of the picture and frame, together?
Answer:
Perimeter of the picture and frame = 38.4inches
Area of the picture and frame = 92.16inches²
Step-by-step explanation:
A square frame is made up of 4 different pieces. The shape of each piece = Rectangle
The perimeter of the rectangle = 24
Perimeter of the rectangle = 24 inches
The perimeter of a rectangle = 2L + 2W
The Width of a Rectangle is always on her than the length hence.
24 = 2L + 2W
24 = 2( L + W)
24/2 = L + W
12 = L + W
Because the width is always longer than the length
W > L
Width of wooden frame = 4 × Length
Therefore;
4 × L = W
Which gives
L + W = 12 inches
4 × L + L = 12 inches
L×(4 + 1)
= 5L = 12 inches
L = 12/5 = 2.4 inches
W = 4 × L = 4 × 12/5
W = 48/5 = 9.6 inches
Side length of wooden frame, L =9.6
The perimeter of the picture frame = 4 × L= 4 × 9.6= 38.4 inches
The area of the picture frame = L²
= L × L
= 9.6 × 9.6 = 92.16inches².
An exterior angle of a triangle is 120° and one of the interior opposite angle is 50°. Find the other two angles of the triangle.
Answer:
interior angle (2)= 70
interior angle (3)= 60
Step-by-step explanation:
Given:
exterior angle=120°
interior angle (1)=50°
Required:
interior angle (2)=?
interior angle (3)=?
Formula:
exterior angle=interior angle (1) + interior angle (2)
Solution:
exterior angle=interior angle (1)+ interior angle (2)
120°=50°+interior angle (2)
120°+50°=interior angle (2)
70°=interior angle (2)
interior angle (3)= 180°-interior angle (1)- interior angle (2)
interior angle (3)=180°-50°+70°
interior angle (3)=180°-120°
interior angle (3)= 60°
Theorem:
Theorem 1.16
The measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
Hope this helps ;) ❤❤❤
As the Type II error, β,of a statistical test increases, the power of the test _____________.
Answer:
decreases.
Step-by-step explanation:
Type II error is one in which we fail to reject the null hypothesis that is actually false. Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The power of Type II error is 1 - [tex]\beta[/tex]. As the power increases the probability of Type II error decreases.
You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately 60%. You would like to be 98% confident that your estimate is within 2.5% of the true population proportion. How large of a sample size is required?
Answer:
A sample size of 2080 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
Based on previous evidence, you believe the population proportion is approximately 60%.
This means that [tex]\pi = 0.6[/tex]
How large of a sample size is required?
We need a sample of n.
n is found when [tex]M = 0.025[/tex]. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.025 = 2.327\sqrt{\frac{0.6*0.4}{n}}[/tex]
[tex]0.025\sqrt{n} = 2.327\sqrt{0.6*0.4}[/tex]
[tex]\sqrt{n} = \frac{2.327\sqrt{0.6*0.4}}{0.025}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.327\sqrt{0.6*0.4}}{0.025})^{2}[/tex]
[tex]n = 2079.3[/tex]
Rounding up
A sample size of 2080 is needed.
If the 2nd and 5th terms of a
G.P are 6 and 48 respectively,
find the sum of the first four
terms
Answer:
45
Step-by-step explanation:
The n th term of a GP is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
Given a₂ = 6 and a₅ = 48, then
ar = 6 → (1)
a[tex]r^{4}[/tex] = 48 → (2)
Divide (2) by (1)
[tex]\frac{ar^4}{ar}[/tex] = [tex]\frac{48}{6}[/tex] , that is
r³ = 8 ( take the cube root of both sides )
r = [tex]\sqrt[3]{8}[/tex] = 2
Substitute r = 2 into (1)
2a = 6 ( divide both sides by 2 )
a = 3
Thus
3, 6, 12, 24 ← are the first 4 terms
3 + 6 + 12 + 24 = 45 ← sum of first 4 terms
When josh borrowed money, he originally agreed to repay the loan by making three equal payments of $1500, with a payment due now, another payment due two years from now, and the final payment due four years from now. Instead of the original payments, he plans to pay off the loan by making a single payment of 5010. If interest is 10%, compounded annually, when will he make the single payment?
Answer:
5 years
Step-by-step explanation:
Principal Amount to be paid=$4500
Interest rate = 2%
Number if Times compounded= number of years
Number of years = x
Among total= $5010
A= p(1+r/n)^(nt)
But n= t =x
A= p(1+r/x)^(x²)
5010=4500(1+0.02/x)^(x²)
5010/4500 = (1+0.02/x)^(x²)
1.11333=( 1+0.02/x)^(x²)
Using trial and error method the number of years maximum to give approximately $5010 is 5 years
6th grade math, help me pleasee:)
Answer:
8 pounds
Step-by-step explanation:
2 x 3 = 6 tb of chili powder in pot 2
find pounds per tablespoon: 48 / 6 = 8 pounds
Answer:
1/2 pound per tablespoon
Step-by-step explanation:
Jaden sure does like his chili!
In the first and second pot, he uses 3 pounds worth of ground beef, which means, 12 ounces of something is a pound. And because Jaden had used 3 times the amount of chili powder in the second pot, he used 6 tablespoons worth of powder. 3 pounds divided by 6 equals 1/2.
What is the missing side lenght in the triangle below?
Answer:
45
Step-by-step explanation:
Let's call the missing side x
This is a right triangle and in right triangles the square length of hypotenuse is equal to sum of square length of base and side lengths
53^2 = 28^2 + x^2
x = 45
Betty and Karen have been hired to paint the houses in a new development. Working together, the women can paint a house in two-thirds the time that it takes Karen working alone. Betty takes 14 h to paint a house alone. Betty takes 6 h to paint a house alone.
Required:
How long does it take Karen to paint a house working alone?
Answer: 3 hours
Step-by-step explanation:
Here is the correct question:
Betty and karen have been hired to paint the houses in a new development. Working together the women can paint a house in two thirds the time that it takes karen working alone. Betty takes 6 hours to paint a house alone. How long does it take karen to paint a house working alone?
Since Betty takes 6 hours to paint a house alone, that means she can paint 1/6 of the house in 1 hour.
Karen can also paint 1/x in 1 hour
Both of them will paint the house in 3/2 hours.
We then add them together which gives:
1/6 + 1/x = 3/2x
The lowest common multiple is 6x
1x/6x + 6/6x = 9/6x
We then leave out the denominators
1x + 6 = 9
x = 9 - 6
x = 3
Karen working alone will paint a house in 3 hours.
The radius of a nitrogen atom is 5.6 × 10-11 meters, and the radius of a beryllium atom is 1.12 × 10-10 meters. Which atom has a larger radius, and by how many times is it larger than the other?
Answer:
The beryllium atom; 1.99 times larger.
Step-by-step explanation:
The beryllium atom is 0.000000000112 meters, while the nitrogen atom is 0.000000000056 meters. So, the beryllium atom is larger than the other.
(1.12 * 10^-10) / (5.6 * 10^-11)
= (1.112 / 5.6) * (10^-10 + 11)
= 0.1985714286 * 10
= 1.985714286 * 10^0
So, the beryllium atom is about 1.99 times larger than the other.
Hope this helps!
The value of y varies inversely as the square of x, and y = 16, when I = 3.
Find the value of x when y = 1.
Answer:
x = 12Step-by-step explanation:
The statement
The value of y varies inversely as the square of x is written as
[tex]y = \frac{k}{ {x}^{2} } [/tex]
where k is the constant of proportionality
To find the value of x when y = 1 first find the formula for the variation
y = 16 x = 3
k = yx²
k = 16(3)²
k = 16 × 9
k = 144
The formula for the variation is
[tex]y = \frac{144}{ {x}^{2} } [/tex]
when y = 1
We have
[tex]1 = \frac{144}{ {x}^{2} } [/tex]
Cross multiply
x² = 144
Find the square root of both sides
We have the final answer as
x = 12Hope this helps you
What is the equation for the plane illustrated below?
Answer:
Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].
Step-by-step explanation:
The general equation in rectangular form for a 3-dimension plane is represented by:
[tex]a\cdot x + b\cdot y + c\cdot z = d[/tex]
Where:
[tex]x[/tex], [tex]y[/tex], [tex]z[/tex] - Orthogonal inputs.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex], [tex]d[/tex] - Plane constants.
The plane presented in the figure contains the following three points: (2, 0, 0), (0, 2, 0), (0, 0, 3)
For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:
xy-plane (2, 0, 0) and (0, 2, 0)
[tex]y = m\cdot x + b[/tex]
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - x-Intercept, dimensionless.
If [tex]x_{1} = 2[/tex], [tex]y_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]y_{2} = 2[/tex], then:
Slope
[tex]m = \frac{2-0}{0-2}[/tex]
[tex]m = -1[/tex]
x-Intercept
[tex]b = y_{1} - m\cdot x_{1}[/tex]
[tex]b = 0 -(-1)\cdot (2)[/tex]
[tex]b = 2[/tex]
The equation of the line in the xy-plane is [tex]y = -x+2[/tex] or [tex]x + y = 2[/tex], which is equivalent to [tex]3\cdot x + 3\cdot y = 6[/tex].
yz-plane (0, 2, 0) and (0, 0, 3)
[tex]z = m\cdot y + b[/tex]
[tex]m = \frac{z_{2}-z_{1}}{y_{2}-y_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
If [tex]y_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]y_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:
Slope
[tex]m = \frac{3-0}{0-2}[/tex]
[tex]m = -\frac{3}{2}[/tex]
y-Intercept
[tex]b = z_{1} - m\cdot y_{1}[/tex]
[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]
[tex]b = 3[/tex]
The equation of the line in the yz-plane is [tex]z = -\frac{3}{2}\cdot y+3[/tex] or [tex]3\cdot y + 2\cdot z = 6[/tex].
xz-plane (2, 0, 0) and (0, 0, 3)
[tex]z = m\cdot x + b[/tex]
[tex]m = \frac{z_{2}-z_{1}}{x_{2}-x_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - z-Intercept, dimensionless.
If [tex]x_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:
Slope
[tex]m = \frac{3-0}{0-2}[/tex]
[tex]m = -\frac{3}{2}[/tex]
x-Intercept
[tex]b = z_{1} - m\cdot x_{1}[/tex]
[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]
[tex]b = 3[/tex]
The equation of the line in the xz-plane is [tex]z = -\frac{3}{2}\cdot x+3[/tex] or [tex]3\cdot x + 2\cdot z = 6[/tex]
After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:
[tex]a = 3[/tex], [tex]b = 3[/tex], [tex]c = 2[/tex], [tex]d = 6[/tex]
Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].
Answer:
It is A 3x+3y+2z=6
Step-by-step explanation:
Leechtown Co. has 4.3% coupon bonds on the market with 18 years left to maturity. The bonds make annual payments. If the bond currently sells for $870, what is its YTM? (Do not round intermediate calculations. Round the final answer to 2 decimal places.) Yield to maturity %
Answer:
YTM = 5.45%
Step-by-step explanation:
Here, we are interested in calculating the yield to maturity.
Mathematically;
Annual coupon=1000*4.3%=43
YTM=[Annual coupon+(Face value-Present value)/time to maturity]/(Face value+Present value)/2
=[43+(1000-870)/18]/(1000+870)2
=5.45%
omplete)
HWS
X 3.3.13-BE
The manufacturer's suggested retail price (MSRP) for a particular car is $25,495, and it is expected to be worth $20,081 in 2 years.
(a) Find a linear depreciation function for this car.
(b) Estimate the value of the car 4 years from now.
(c) At what rate is the car depreciating?
(a) What is the linear depreciation function for this car?
f(x) =
(Simplify your answer. Do not include the $ symbol in your answer.)
Answer:
a) y = 25495 - 2707x
b) y = 25495 - 2707(4) = 14,667
c) $2,707 per year
Step-by-step explanation:
Value now: $25,495
Value in 2 years: $20,081
Loss of value in 2 years: $25,495 - $20,081 = $5,414
Loss of value per year: $5,414/2 = $2,707
a) y = 25495 - 2707x
b) y = 25495 - 2707(4) = 14,667
c) $2,707 per year
Which steps can be used in order to determine the solution to Negative 1.3 + 4.6 x = 0.3 + 4 x?
Answer:
x=8/3 OR 2.7
Step-by-step explanation:
-1.3+4.6x=0.3+4x
4.6x-4x=0.3+1.3
0.6x=1.6
x=1.6/0.6=8/3
x=8/3 OR 2.7
Hope this helps!
Answer:
[tex]\boxed{x = 2\frac{2}{3} }[/tex]
Step-by-step explanation:
[tex]-1.3+4.6x = 0.3 +4x[/tex]
Collecting like terms
[tex]4.6 x -4x = 0.3+1.3[/tex]
[tex]0.6x = 1.6[/tex]
Dividing both sides by 0.6
x = 1.6 / 0.6
x = 2 2/3
The length of a rectangle is four times its width. If the perimeter of the rectangle is 50 yd, find its area
Answer:
100yd²
Step-by-step explanation:
length=4x
width=x
perimeter=2(l+w)
50=2(4x+x)
50=2(5x)=10x
50=10x
x=5yd
width=5yd
length=20yd
area=length×width
=20×5
=100yd²
Answer:
[tex]\boxed{\red{100 \: \: {yd} ^{2}}} [/tex]
Step-by-step explanation:
width = x
length = 4x
so,
perimeter of a rectangle
[tex] p= 2(l + w) \\ 50yd = 2(4x + x) \\ 50yd= 2(5x) \\ 50yd= 10x \\ \frac{50yd}{10} = \frac{10x}{10} \\ x = 5 \: \: yd[/tex]
So, in this rectangle,
width = 5 yd
length = 4x
= 4*5
= 20yd
Now, let's find the area of this rectangle
[tex]area = l \times w \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20 \times 5 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 100 {yd}^{2} [/tex]
Six human skulls from around 4000 b.c. were measured, and the lengths have a mean of 94.2 mm and a standard deviation of 4.9
mm. If you want to construct a 95% confidence interval estimate of the mean length of all such skulls, assume that the requirements
are satisfied. Find the critical values that would be used to construct a 95% confidence interval estimate of o
Answer:
Step-by-step explanation:
Hello!
You have to estimate the mean length of 4000 b.c. human skulls trough a 95% confidence interval.
You know that
n= 6 human skulls
[tex]\frac{}{X}[/tex]= 94.2mm
S= 4.9
Assuming that the variable X: length of a 4000b.c. human skull (mm) has a normal distribution, to construct the interval you have to use the t statistic:
[[tex]\frac{}{X}[/tex] ± [tex]t_{n_1;1-\alpha /2} * \frac{S}{\sqrt{n} }[/tex]]
[tex]t_{n-1;1-\alpha /2}= t_{5; 0.975}= 2.571[/tex]
[94.2 ± 2.571 * [tex]\frac{4.9}{\sqrt{6} }[/tex]]
[89.06; 99.34]mm
With a 95% confidence level you'd expect the interval [89.06; 99.34]mm to contain the value for the average skull length for humans 4000 b.c.
I hope this helps!
Which number line represents the solution set for the inequality 3(8 - 4x) < 6(x - 5)?
Answer:
x>3
Step-by-step explanation:
Find the exact values of sin 2θ and cos 2θ for cos θ = 6/13
Answer:
Step-by-step explanation:
cos^-1(6/13)=62.5136°
sin(2*62.5136°)=0.8189
cos(2*62.5136°)=-0.5740
Find the area under the standard normal curve to the right of z = 2.
Answer:
0.0228
Step-by-step explanation:
A suitable probability calculator (or spreadsheet) can tell you this.
It is about 0.0228.
Find the total surface area of the cone in the figure. ( use rr=3.14.)
Answer:
Answer D
Step-by-step explanation:
The formula is [tex]A = pi r(r+\sqrt{h^2+r^2})[/tex]. We have our r (radius) and h (height), so plugging it all in would give us A = (3.14)(5 + sqrt(12^2)+(5^2). After computing this, you would get answer D, 282.6.
Express 0.325 as a percentage
Answer:
32.5%
Step-by-step explanation:
0.325 x 100%=32.5%
What is the solution for x in the given equation? (root)9x+7+ (root)2x=7 A. x = 18 and x = 2 B. x = 18 C. x = 2 D. x = 18 and x = -2
Answer:
C. x = 2
Step-by-step explanation:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
Since you have square roots, you need to separate the square roots and square both sides.
[tex] \sqrt{9x + 7} = 7 - \sqrt{2x} [/tex]
Now that one square root is on each side of the equal sign, we square both sides.
[tex] (\sqrt{9x + 7})^2 = (7 - \sqrt{2x})^2 [/tex]
[tex] 9x + 7 = 49 - 14\sqrt{2x} + 2x [/tex]
Now we isolate the square root and square both sides again.
[tex] 7x - 42 = -14\sqrt{2x} [/tex]
Every coefficient is a multiple of 7, so to work with smaller numbers, we divide both sides by 7.
[tex] x - 6 = -2\sqrt{2x} [/tex]
Square both sides.
[tex] (x - 6)^2 = (-2\sqrt{2x})^2 [/tex]
[tex] x^2 - 12x + 36 = 4(2x) [/tex]
[tex] x^2 - 20x + 36 = 0 [/tex]
We need to try to factor the left side.
-2 * (-18) = 36 & -2 + (-18) = -20, so we use -2 and -18.
[tex] (x - 2)(x - 18) = 0 [/tex]
[tex] x = 2 [/tex] or [tex] x = 18 [/tex]
Since solving this equation involved the method of squaring both sides, we much check for extraneous solutions by testing our two solutions in the original equation.
Test x = 2:
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(2) + 7} + \sqrt{2(2)} = 7 [/tex]
[tex] \sqrt{25} + \sqrt{4} = 7 [/tex]
[tex] 5 + 2 = 7 [/tex]
[tex] 5 = 5 [/tex]
We have a true equation, so x = 2 is a true solution of the original equation.
Now we test x = 18.
[tex] \sqrt{9x + 7} + \sqrt{2x} = 7 [/tex]
[tex] \sqrt{9(18) + 7} + \sqrt{2(18)} = 7 [/tex]
[tex] \sqrt{162 + 7} + \sqrt{36} = 7 [/tex]
[tex] \sqrt{169} + 6 = 7 [/tex]
[tex] 13 + 6 = 7 [/tex]
[tex] 19 = 7 [/tex]
Since 19 = 7 is a false equation, x = 18 is not a true solution of the original equation and is discarded as an extraneous solution.
Answer: C. x = 2
g Find the mean and the variance of the random variable X with probability function or density f(x) of a uniform distribution on [0, 8].
Answer: E(X) = 4
V(X) = [tex]\frac{16}{3}[/tex]
Step-by-step explanation: An uniform distribution is a random variable X restricted to a finite interval [a,b] and has a constant function f(x) over this interval, i.e., the function is of form:
f(x) = [tex]\left \{ {{\frac{1}{b-a} } \atop {0}} \right.[/tex]
The mean or expectation of an unifrom distribution is:
E(X) = [tex]\int\limits^b_a {x.f(x)} \, dx[/tex]
For the density function in interval [0,8], expectation value is:
E(X) = [tex]\int\limits^8_0 {x.(\frac{1}{8-0} )} \, dx[/tex]
E(X) = [tex]\int\limits^8_0 {\frac{x}{8} } \, dx[/tex]
E(X) = [tex]\frac{1}{8}. \int\limits^8_0 {x} \, dx[/tex]
E(X) = [tex]\frac{1}{8}.(\frac{x^{2}}{2} )[/tex]
E(X) = [tex]\frac{1}{8} (\frac{8^{2}}{2} )[/tex]
E(X) = 4
Variance of a probability distribution can be written as:
V(X) = [tex]E(X^{2}) - [E(X)]^{2}[/tex]
For uniform distribution in interval [0,8]:
V(X) = [tex]\int\limits^b_a {x^{2}.\frac{1}{8-0} } \, dx - (\frac{8+0}{2})^{2}[/tex]
V(X) = [tex]\frac{1}{8} \int\limits^8_0 {x^{2}} \, dx - 4^{2}[/tex]
V(X) = [tex]\frac{1}{8} (\frac{x^{3}}{3} ) - 16[/tex]
V(X) = [tex]\frac{1}{8} (\frac{8^{3}}{3} ) - 16[/tex]
V(X) = [tex]\frac{64}{3}[/tex] - 16
V(X) = [tex]\frac{16}{3}[/tex]
The mean and variance are 4 and 16/3, respectively
Which of the following graphs is described by the function below ?
Answer:
The point of interception of the graph and x axis are -2.366 and -0.634.
The only graph that satisfy this conditions is Graph A
Step-by-step explanation:
Given the equation;
[tex]y = 2x^2 + 6x + 3\\[/tex]
at y = 0
[tex]2x^2 + 6x + 3=0\\[/tex]
the roots of the quadratic equation (at y =0) can be calculated using the quadratic formula;
[tex]x = \frac{-b\pm \sqrt{b^2 -4ac}}{2a}[/tex]
Using the quadratic equation to solve for the roots;
[tex]x = \frac{-6\pm \sqrt{6^2 -4*2*3}}{2*2}\\x = \frac{-6\pm \sqrt{36 - 24}}{4}\\x = \frac{-6\pm \sqrt{12}}{4}\\so, we have \\x = -2.366\\or\\x = -0.634\\[/tex]
Therefore, the point of interception of the graph and x axis are -2.366 and -0.634.
The only graph that satisfy this conditions is Graph A
x−15≤−6 solve for x pls help
Answer:
x≤9
Step-by-step explanation:
x−15≤−6
Add 15 to each side
x−15+15≤−6+15
x≤9
Answer:
[tex]\boxed{x\leq 9}[/tex]
Step-by-step explanation:
[tex]x-15 \leq -6[/tex]
[tex]\sf Add \ 15 \ to \ both \ parts.[/tex]
[tex]x-15 +15 \leq -6+15[/tex]
[tex]x\leq 9[/tex]
Louden County Wildlife Conservancy counts butterflies each year. Data over the last three years regarding four types
of butterflies are shown below. What is the average number of Variegated Fritillaries for all three samples?
A. 55 B.83 C.106 D.165
Answer:
A). 55
Step-by-step explanation:
Number of Variegated Fritillaries for each year is
2009 = 7
2010= 95
2011= 63
The sum total of the samples= 7+95+63
The sum total of the samples= 165
Number of years= 3
The average= total/number of years
The average= 165/3
The average= 55
Answer: A
Step-by-step explanation: I have a massive brain (•-*•)
A line passes through the points (6, 10) and (4, -2). What is the equation of the line
Answer:
y = 6x - 26
Step-by-step explanation:
1. find slope: (y₂ - y₁) / (x₂ - x₁)
(-2 - 10) / (4 - 6) = -12 / -2 = 6
basic equation: y = 6x + b
2. plug in (x,y) value using one set of coordinates.
10 = 6(6) + b
10 = 36 + b
b = 10 - 36
b = -26
3. plug b in to find full equation.
y = 6x -26
Answer:
y = -1/6 x + 11
Step-by-step explanation:
In order to write an equation of a line you need slope (m) and y-intercept (b) or where the graph grosses the y- axis. since you are given two points (6, 10) and (4, -2). Slope when given two points is (y - y) / (x - x)
so (-2 - 10) / (6 - 4) = 6 / - 1 =- 6
use the equation y = mx + b and substitute either point (6, 10) or (4, -2) as a replacement for x and y respectively. (I chose (6, 10) because they are positive numbers. Substituting x = 6 and y = 10 and m = -6 into y = mx + b
10 = -6(6) + b
10 = -36 + b
b = 46 (add -36 to both sides)
so our equation: y = -6x + 46 :-)
Please answer this correctly without making mistakes
Answer:
41.1 miles
Step-by-step explanation:
84 - 42.9 = 41.1
the product of two consequtive integers is 72 the equation x(x+1)=72 represents the situation, where x represents the smaller integer, which equation can be factor and solve for the smaller integer?
Answer:
x² + x - 72 = 0 can be factored into (x - 8)(x + 9) = 0 to find your answer.
Step-by-step explanation:
Step 1: Distribute x
x² + x = 72
Step 2: Move 72 over
x² + x - 72 = 0
Step 3: Factor
(x - 8)(x + 9) = 0
Step 4: Find roots
x - 8 = 0
x = 8
x + 9 = 0
x = -9
Answer:
x² + x - 72 = 0 ⇒ (x - 8)(x + 9) = 0
Step-by-step explanation:
Let the first consecutive integer be x.
Let the second consecutive integer be x+1.
The product of the two consecutive integers is 72.
x(x + 1) = 72
x² + x = 72
Subtracting 72 from both sides.
x² + x - 72 = 0
Factor left side of the equation.
(x - 8)(x + 9) = 0
Set factors equal to 0.
x - 8 = 0
x = 8
x + 9 = 0
x = -9
8 and -9 are not consecutive integers.
Try 8 and 9 to check.
x = 8
x + 1 = 9
x(x+1) = 72
8(9) = 72
72 = 72
True!
The two consecutive integers are 8 and 9.