Answer:
I = P/V
Step-by-step explanation:
To find the equation solved for in terms of I, simply divide both sides by V to get V and P in terms of I.
The hardware store where you work charge 80 cents including tax, for a pound of nails. A customer purchases 5 3/4 pound of nails. How much should you charge the customer for nails?
Answer:
4.60
Step-by-step explanation:
multiply 5.75 and 0.80 to get 4.60
Answer:
460
Step-by-step explanation:
x/80 = 5 3/4 or 23/4
23*80= 1,840
1,840/4 = 460
Determine the sum of the arithmetic series 6 + 11 + 16 +......
91.
Answer:
873
Step-by-step explanation:
so the equation is: 5x+1
sum is:
[tex] \frac{first \: one \: + \: last \: one}{2} \times quantity \: of \: terms \\ [/tex]
we have 6( 5×1+1) to 91 (5×18+1)
so we have 18 terms
then:
[tex] \frac{91 + 6}{2} \times 18 = 873[/tex]
Circles c and c are similar state the translation rule and the scale factor of dilation
To obtain circle C', circle C was translated to the right 3 units and down 2 units, then dilated by a scale factor of 2
What is a transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.
Dilation is the increase or decrease in the size of a figure.
To obtain circle C', circle C was translated to the right 3 units and down 2 units, then dilated by a scale factor of 2
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Problem of the Day
The tortoise and the hare were arguing: who's the fastest? The tortoise boasted he
could swim 220 miles in 10 hours. The hare bragged he could hop 90 miles in 2 hours.
But who is faster? How can you tell?
Answer:
hare
Step-by-step explanation:
Their average rates are ...
tortoise: (220 mi)/(10 h) = 22 mi/h
hare: (90 mi)/(2 h) = 45 mi/h
The hare has a faster speed than the tortoise.
Given that 20 − (y − x) = 30 − (x − y), and x = 4, what is the value of y ?
Step-by-step explanation:
when you substitute x for four then you collect like terms
I hope it helps
Simplify the slope of AC
Answer:
[tex]Slope\:\: \overline{AC} =1[/tex]
Step-by-step explanation:
A is on the same point on the x-axis as B and the same point on the y-axis as D
Therefore, the coordinate of A is (0,0)C is on the same point on the x-axis as D and the same point on the y-axis as B.
Therefore, the coordinate of C is (a,a)We are to determine the slope of the line joining A to C.
[tex]Slope, m =\dfrac{y_2-y_1}{x_2-x_1} \\(x_1,y_1)=(0,0),(x_2,y_2)=(a,a)\\$Therefore, Slope of AC$\\m =\dfrac{a-0}{a-0}\\=\dfrac{a}{a}\\\\=1[/tex]
[tex]Slope\:\: \overline{AC} =1[/tex]
Which shapes have the same volume as the given rectangular prism?
base area = 50 cm^2
Answer:The first one
Step-by-step explanation:
V rectangular prism = Area of the base *5
A Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer; a sample of 700 men (unrelated to the women) ages 18-29 found that 133 men said that they had the most say when purchasing a computer. Test whether there is a difference between these proportions at α = 0.05. What is the test statistic value? Group of answer choices
Answer:
Step-by-step explanation:
Step(i):-
Given first random sample size n₁ = 500
Given Roper survey reported that 65 out of 500 women ages 18-29 said that they had the most say when purchasing a computer.
First sample proportion
[tex]p^{-} _{1} = \frac{65}{500} = 0.13[/tex]
Given second sample size n₂ = 700
Given a sample of 700 men (unrelated to the women) ages 18-29 found that 133 men said that they had the most say when purchasing a computer.
second sample proportion
[tex]p^{-} _{2} = \frac{133}{700} = 0.19[/tex]
Level of significance = α = 0.05
critical value = 1.96
Step(ii):-
Null hypothesis : H₀: There is no significance difference between these proportions
Alternative Hypothesis :H₁: There is significance difference between these proportions
Test statistic
[tex]Z = \frac{p_{1} ^{-}-p^{-} _{2} }{\sqrt{PQ(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }[/tex]
where
[tex]P = \frac{n_{1} p^{-} _{1}+n_{2} p^{-} _{2} }{n_{1}+ n_{2} } = \frac{500 X 0.13+700 X0.19 }{500 + 700 } = 0.165[/tex]
Q = 1 - P = 1 - 0.165 = 0.835
[tex]Z = \frac{0.13-0.19 }{\sqrt{0.165 X0.835(\frac{1}{500 } +\frac{1}{700 } )} }[/tex]
Z = -2.76
|Z| = |-2.76| = 2.76 > 1.96 at 0.05 level of significance
Null hypothesis is rejected at 0.05 level of significance
Alternative hypothesis is accepted at 0.05 level of significance
Conclusion:-
There is there is a difference between these proportions at α = 0.05
According to the question,
Women,
[tex]\hat p_1 = \frac{65}{500}[/tex][tex]= 0.13[/tex]
Men,
[tex]\hat p_2=\frac{300}{700}[/tex][tex]= 0.19[/tex]
Now,
The pooled estimate of the proportion will be:
→ [tex]\hat p=\frac{x_1+x_2}{n_1+n_2}[/tex]
By substituting the values,
[tex]= \frac{65+133}{500+700}[/tex]
[tex]= 0.165[/tex]
then,
→ [tex]\hat q = 1- \hat p[/tex]
[tex]= 1- 0.165[/tex]
[tex]= 0.835[/tex]
hence,
The test statistics:
→ [tex]Z = \frac{\hat p_1- \hat p_2}{\sqrt{\hat p\times \hat q\times (\frac{1}{n_1} +\frac{1}{n_2} )} }[/tex]
By putting the values, we get
[tex]= \frac{0.13-0.19}{\sqrt{0.165\times 0.835\times (\frac{1}{500} +\frac{1}{700} )} }[/tex]
[tex]= -2.76[/tex]
Thus the above response is right.
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You buy halibut at $30 per
pound,
One portion of seared
halibut requires 6 ounces of
halibut.
How much does the halibut
for one portion cost? Round
to the nearest cent.
Answer:
$11.25
Step-by-step explanation:
price = $30/lb
16 oz = 1 lb
1 portion = 6 oz = 6/16 lb = 3/8 lb
$30/lb * 3/8 lb = $11.25
what is 18576939*47 Thanks!!!!!
Answer:
873116133
Step-by-step explanation:
18576939 × 47
Multiply the numbers.
= 873116133
Answer: 873116133
Step-by-step explanation:
‘Hope this helps:)
The number of bacteria, B(h), in a certain population increases according to the following
function, where time, h, is measured in hours:
B(h) = 1425 e ^0.15h
How many hours will it take for the bacteria to reach 3300?
Round your answer to the nearest tenth, and do not round any intermediate
computations.
Please helpppp!!!
Answer:
It will take 5.6 hours to get the given population (3300) of the bacteria.
Step-by-step explanation:
A function that defines the population increase of a bacteria is,
B(h) = [tex]1425e^{0.15h}[/tex]
where h = duration or number of hours for bacterial growth
B(h) = Final population
If the final bacterial population is 3300,
3300 = [tex]1425e^{0.15h}[/tex]
By taking log on both the sides of the equation,
ln(3300) = [tex]ln(1425e^{0.15h})[/tex]
8.10168 = ln(1425) + [tex]ln(e^{0.15h})[/tex]
8.10168 = 7.261927 + 0.15h
h = [tex]\frac{8.10168-7.261927}{0.15}[/tex]
h = 5.5983
h ≈ 5.6 hours
Therefore, it will take 5.6 hours to get the given population (3300) of the bacteria.
please help me on number 11 if you know how to :) !
Answer:
(x, y) = (25, 18)
Step-by-step explanation:
Use the angle sum theorem. You can write equations for the right angle and for the linear angle.
(x +11) +(3y) = 90 . . . . sum of angles making the right angle
(y +7) +90 +65 = 180 . . . . sum of angles making the linear angle
From the second equation, we have ...
y = 18 . . . . subtract 162
Substituting into the first equation gives ...
x + 11 + 3(18) = 90
x = 25 . . . . subtract 65
The values of x and y are 25 and 18, respectively.
_____
Check
VQ = 18+7 = 25
QR = 25 +11 = 36
RS = 3·18 = 54
ST = 65
The totals are 36 +54 = 90; 25 +36 +54 +65 = 180, as required.
Find the inequality represented by the graph.
Answer:
[tex]x \geqslant \frac{y + 4}{3} [/tex]Explanation;
Associated line with this equation is:
y=mx+c
when,
X=0
y=-4
so, c=-4
X=1
y=-1
[tex] - 1 = m- 4 \\ - m = - 4 + 1 \\ - m = - 3 \\ m =3 \\ [/tex]
[tex]y = 3x - 4 \\ or \: y + 4 = 3x \\ or \: \frac{y + 4}{3} = x[/tex]
Inequality representated by graph:
[tex]x \geqslant \frac{y + 4}{3} [/tex]
Hope this helps...
Good luck on your assignment...
Find the value of x in each of the following exercises:
Answer:
x = 25
Step-by-step explanation:
you just work out all of the degrees in the other triangles first
Stat 3309 - Statistical Analysis for Business Applications I
Consider the following data representing the starting salary (in $1,000) at some company and years of prior working experience in the same ï¬eld. The sample of 10 employees was taken and the following data is reported.
Years of experience
Starting Salary (in $1,000)
0
45
2 50
5 55
7 62
8 63
10 70
12 68
15 75
18 81
20 92
Part 1: Use the formulas provided on the 3rd formula sheet to compute the following quantities. Open an Excel spreadsheet and write the table with data given above. Add columns for x2, y2, and xy, as well as the last row for Σ. For each of the following quantities, write the formula for it in a cell and evaluate it.
(a) Find the sample correlation coeï¬cient r.
(b) Find the slope b1 of the sample regression line.
(c) Find the y-intercept b0 of the sample regression line.
(d) What is the equation of the sample regression line?
(e) Find the predicted starting salary for a person who spent 15 years working in the same ï¬eld.
(f) Find the observed starting salary for a person who spent 15 years working in the same ï¬eld.
(g) What is the diï¬erence between the observed and the predicted starting salary for a person who spent 15 years working in the same ï¬eld?
(h) Find the total sum of squares SST.
(i) Find the sum of squares error SSE.
(j) Find the sum of squares regression SSR.
(k) Use the answers from (h)-(j) to conï¬rm that SST = SSR + SSE. (l) Find the coeï¬cient of determination R2.
(m) Use your answers for (a), (b) and (l), to conï¬rm that r = ±âR2.
(n) What proportion of variation is explained using the regression model?
(o) Find the standard error of the estimate se.
(p) Find the standard error of the regression slope sb.
(q) Does the number of years of prior working experience in the same ï¬eld aï¬ect the starting salary at this company ? Use the sample provided above and the signiï¬cance level of 0.05.
(hint: perform the hypothesis test for H0 : β1 = 0 vs. H1 : β1 6= 0.)
Part 2: Find and use Excel built-in-functions to check your answers for r, b1, and b0. Next to each cell from Part 1, calculate these three quantities using Excel built-in-functions and conï¬rm your answers from Part 1.
(hint: for example, for r the Excel built-in function is "CORREL")
Part 3: Bellow your answers from Parts 1 and 2, perform the regression analysis using Excel built-in-module which can be found under "DATA" â "Data Analysis" â "Regression" and double check your answers from Part 1. Draw the scatter plot of the data and, by visually observing the graph, determine if there is a linear relationship between the number of years of prior working experience in the same ï¬eld and the starting salary at this company.
Answer:
Solved below.
Step-by-step explanation:
The data is provided for the starting salary (in $1,000) at some company and years of prior working experience in the same field for randomly selected 10 employees.
(a)
The formula to compute the correlation coefficient is:
[tex]r=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\[/tex]
The required values are computed in the Excel sheet below.
[tex]\begin{aligned}r~&=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\r~&=~\frac{ 10 \cdot 7252 - 97 \cdot 661 } {\sqrt{\left[ 10 \cdot 1335 - 97^2 \right] \cdot \left[ 10 \cdot 45537 - 661^2 \right] }} \approx 0.9855\end{aligned}[/tex]
Thus, the sample correlation coefficient r is 0.9855.
(b)
The slope of the regression line is:
[tex]b_{1} &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 10 \cdot 7252 - 97 \cdot 661 }{ 10 \cdot 1335 - \left( 97 \right)^2} \\\\\approx 2.132[/tex]
Thus, the slope of the regression line is 2.132.
(c)
The y-intercept of the line is:
[tex]b_{0} &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 661 \cdot 1335 - 97 \cdot 7252}{ 10 \cdot 1335 - 97^2} \\\\\approx 45.418[/tex]
Thus, the y-intercept of the line is 45.418.
(d)
The equation of the sample regression line is:
[tex]y=45.418+2.132x[/tex]
(e)
Compute the predicted starting salary for a person who spent 15 years working in the same field as follows:
[tex]y=45.418+2.132x\\\\=45.418+(2.132\times15)\\\\=45.418+31.98\\\\=77.398\\\\\approx 77.4[/tex]
Thus, the predicted starting salary for a person who spent 15 years working in the same field is $77.4 K.
Answer:
Yes correct
Step-by-step explanation:
I think this is correct becase: 2 50
5 55
7 62
etc
these are all correct
The length of a rectangle is 4 inches more than its width. The area of the rectangle is equal to 5 inches more than 2 times the perimeter. Find the length and width if the rectangle.
Answer:
Length: sqrt13 + 4
Width: sqrt13
Step-by-step explanation:
Denote the width as x, then the length is x+4. The area of the rectangle will be x(x+4), and the perimeter will then be 4x +8. Hence, you can write the equation x(x+4) - 5 = 4x+8. Solving, you get x = sqrt13.
The length of the rectangle is 11 inches and width is 7 inches.
From the first statement, the length of the rectangle is 4 inches more than its width,
Let the length be [tex]l[/tex] and the width be [tex]w[/tex]
Then,
[tex]l = 4 +w[/tex] ------ (1)
From the second statement, the area of the rectangle is equal to 5 inches more than 2 times the perimeter
Then,
[tex]A = 5 + 2P[/tex] ----- (2)
Let the area be [tex]A[/tex] and the perimeter be [tex]P[/tex]
But, area of rectangle is given by the formula
[tex]A = l \times w = lw[/tex]
and the perimeter of a rectangle is given by
[tex]P = 2(l+w)[/tex]
Putting these into equation (2),
[tex]A = 5 + 2P[/tex]
we get
[tex]lw = 5 + 2[2(l+w)][/tex]
[tex]lw = 5 + 2 (2l+2w)[/tex]
[tex]lw = 5 + 4l +4w[/tex] ------ (3)
From equation (1)
[tex]l = 4 +w[/tex]
Substitute this into equation (3)
[tex]lw = 5 + 4l +4w[/tex]
[tex](4+w)w = 5 + 4(4+w) +4w\\4w + w^{2} = 5 + 16 + 4w + 4w\\w^{2}+4w = 21+8w\\w^{2}+4w -8w-21= 0 \\w^{2}-4w-21= 0[/tex]
Solve the above equation quadratically
[tex]w^{2}-4w-21= 0\\w^{2}-7w+3w-21= 0\\w(w-7)+3(w-7)=0\\(w+3)(w-7)=0\\[/tex]
[tex]w+3 = 0[/tex] or [tex]w-7=0[/tex]
[tex]w= -3[/tex] or [tex]w = 7[/tex]
Since dimension cannot be negative
∴ [tex]w = 7[/tex]
∴width = 7 inches
For the length
Substitute the value of w into equation (1)
[tex]l = 4 +w[/tex]
[tex]l = 4 +7[/tex]
[tex]l = 11[/tex]
∴ length = 11 inches
Hence, the length of the rectangle is 11 inches and width is 7 inches.
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A composite figure is divided into two congruent trapezoids, each with a height of 4 cm. 2 trapezoids. Both trapezoids have base lengths of 10 centimeters and 6 centimeters, and a height of 4 centimeters. Trapezoid area: A = one-half (b 1 + b 2) h What is the area of this composite figure? 32 centimeters squared 40 centimeters squared 64 centimeters squared 80 centimeters squared
Answer:
48 cm^2
Step-by-step explanation:
Problem:
A composite figure is divided into two congruent trapezoids, each with a height of 4 cm. 2 trapezoids. Both trapezoids have base lengths of 10 cm and 6 cm, and a height of 4 cm. Trapezoid area: A = (1/2)(b1 + b2)h What is the area of this composite figure? 32 cm squared 40 cm squared 64 cm squared 80 cm squared
Solution:
The problem gives you all the information you need.
area of trapezoid = A = (1/2)(b1 + b2)h
b1 = 10 cm
b2 = 6 cm
h = 4 cm
Also, keep in mind the composite figure is made up of two trapezoids, so after we find the area of one trapezoid, we will double it to find the total area.
A = (1/2)(10 cm + 6 cm)(4 cm) = 24 cm^2
The area of 1 trapezoid is 24 cm^2.
The total area = 2 * 24 cm^2 = 48 cm^2
Answer:
64cm2
Step-by-step explanation:
I just did the quiz! its option c or 64cm2
Hope this helps
aryy<3
The expression 3 × 7 – 4 × 8 + 2 is equivalent to which of the following?
Answer:
-9
Step-by-step explanation:
3 time 7
minus
4 times 8
21 - 32
-11+2= -9
PLEASE ANSWER ASAP, I I NEED IT
simplify multiply and remove all perfect squares assume x is positive
Answer:
[tex]\large \boxed{\sf \ \ \sqrt{3x^4}\cdot \sqrt{5x^2}\cdot \sqrt{10}=5x^3\sqrt{6} \ \ }[/tex]
Step-by-step explanation:
Hello,
First, of all, as x is positive we know that:
[tex](\sqrt{x})^2=|x|=x[/tex]
Let's simplify the expression:
[tex]\sqrt{3x^4}\cdot \sqrt{5x^2}\cdot \sqrt{10}=\sqrt{3}\cdot x^2\cdot \sqrt{5}\cdot x\cdot \sqrt{2\cdot 5}=x^3\cdot \sqrt{3\cdot 5\cdot 5 \cdot 2}\\ \\=5x^3\sqrt{6}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Find the average variable cost for producing 42 sneakers. Round your answer to the nearest hundredth.
Answer:
The average variable cost for producing 42 sneakers is $2.98 per unit.
Step-by-step explanation:
We have, for 42 sneakers, the following costs:
Fixed costs: $118Variable costs: $125The total cost for 42 snickers is $243.
The average variable cost can be calculated dividing the total variable cost by the number of units.
This, for 42 snickers, is:
[tex]\bar{vc}=\dfrac{VC}{q}=\dfrac{125}{42}\approx2.98[/tex]
Perform the following operations and prove closure. Show your work.
1. x/x+3 + x+2/x+5
2. x+4/x^2+5x+6 • x+3/x^2−16
3. 2/x^2−9 − 3x/x^2−5x+6
4 . x+4/x^2−5x+6 ÷ x^2−16/x+3
Answer:
1. x/x+3 + x+2/x+5
2. x+4/x²+5x+6 • x+3/x²−16
3. 2/x²−9 − 3x/x²−5x+6
4. x+4/x²−5x+6 ÷ x²−16/x+3
Step-by-step explanation:
1. x/x+3 + x+2/x+5
Taking LCM of (x+3) and (x+5) which is: (x+3)(x+5)
[Mathematical symbol unavailable]
Therefore, to prove closure, The value of x≠-3 and x≠-5 because if their values are -3 and -5 then the denominator will be zero.
2. x+4/x²+5x+6 • x+3/x²−16
Factors of x²-16 = (x)² -(4)² = (x-4)(x+4)
Factors of x²+5x+6 = x²+3x+2x+6 = x(x+3)+2(x+3) =(x+2)(x+3)
Putting factors
[Mathematical symbol unavailable]
Therefore, to prove closure, the value of x≠-2 and x≠4 because if their values are -2 and 4 then the denominator will be zero.
3. 2/x²−9 − 3x/x²−5x+6
Factors of x²-9 = (x)²-(3)² = (x-3)(x+3)
Factors of x²-5x+6 = x²-2x-3x+6 = x(x-2)+3(x-2) =(x-2)(x+3)
Putting factors
Taking LCM of (x-3)(x+3) and (x-2)(x+3) we get (x-3)(x+3)(x-2)
[Mathematical symbol unavailable]
Therefore, to prove closure, the value of x≠3 and x≠-3 and x≠2 because if there values are -3,3 and 2 then the denominator will be zero.
4. x+4/x²−5x+6 ÷ x²−16/x+3
Factors of x²-5x+6 = x²-3x-2x+6 = x(x-3)-2(x-3) = (x-2)(x-3)
Factors of x²-16 = (x)² -(4)² = (x-4)(x+4)
Converting ÷ sign into multiplication we will take reciprocal of the second term
[Mathematical symbol unavailable]
Therefore, to prove closure, the value of x≠2 and x≠4 because if their values are 2 and 4 then the denominator will be zero.
The test statistic of zequals2.31is obtained when testing the claim that pgreater than0.9.a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.b. Find the P-value.c. Using a significance level of alphaequals0.10,should we reject Upper H 0or should we fail to reject Upper H 0?
Answer:
Step-by-step explanation:
a) From the information given, we can state the hypothesis as follows:
For null hypothesis,
p = 0.9
Or
p ≤ 0.9
For alternative hypothesis,
p > 0.9
Because of the greater than inequality symbol in the alternative hypothesis, it means that it is a right tailed test.
b) Since z = 2.31, we would determine the p value by looking at the probability corresponding to the area above the z score from the normal distribution table. Thus
P value = 1 - 0.9896 = 0.0104
Using a significance level of alpha equals 0.10, since alpha, 0.10 is > p value, 0.0104, then we would reject the null hypothesis.
. Suppose X ∼ Unif(−1, 3). Find the probabilities of the following events, both by hand calculation and with R’s punif function. (a) (X ≤ 2) (b) (X ≥ 1) (c) (−0.5 < X < 1.5) (d) (X = 0)
Answer:
a) [tex] P(X \leq 2) = \frac{2+1}{3+1}= 0.75[/tex]
b) [tex] P(X \geq 1) = 1- P(X <1) =1-\frac{1+1}{3+1}= 1-0.5=0.5[/tex]
c) [tex]P(-0.5 <X <1.5)= P(X<1.5)- P(X<-0.5)= \frac{1.5+1}{4} -\frac{-0.5+1}{4}=0.625-0.125= 0.5[/tex]
d) [tex] f(x) = \frac{1}{3+1}= 0.25[/tex]
Step-by-step explanation:
Let X the random variable of interest and we know that the distribution is given by:
[tex]X \sim Unif (a= -1, b=3)[/tex]
And for this problem we can use the cumulative distribution function in order to solve the items:
[tex] F(x) =\frac{x-a}{b-a}, a\leq x \leq b[/tex]
Part a
We want to find this probability:
[tex] P(X \leq 2) = \frac{2+1}{3+1}= 0.75[/tex]
Part b
[tex] P(X \geq 1) = 1- P(X <1) =1-\frac{1+1}{3+1}= 1-0.5=0.5[/tex]
Part c
[tex]P(-0.5 <X <1.5)[/tex]
And we can calculate the probability with this difference:
[tex]P(-0.5 <X <1.5)= P(X<1.5)- P(X<-0.5)= \frac{1.5+1}{4} -\frac{-0.5+1}{4}=0.625-0.125= 0.5[/tex]
Part d
Since we have a continuous distribution the the probability for an unique value would be:
[tex] f(x) = \frac{1}{3+1}= 0.25[/tex]
The function f(x)=3x4−x2+7
f
(
x
)
=
3
x
4
−
x
2
+
7
is/has
Answer: the answer is c = 29
Step-by-step explanation:
The function f(x)=3x⁴−x²+7 has the slope of 12x³ - 2x.
What is a function?
A certain kind of relationship called a function binds inputs to essentially one output.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
A function can be regarded as a computer, which is helpful.
Given the function
f(x)=3x⁴−x²+7
The slope of any function at a point is = the first derivative at that point
Since our function is f(x)=3x⁴−x²+7
d[f(x)]/dx = 12x³ - 2x so it will general formula for finding out slope at any point.
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Simplify the expression ( √3+i) + (√5-2i) and write the result in a+bi.
Answer:
c. (√3 + √5) - i
Step-by-step explanation:
(√3+i) + (√5-2i) = √3+i + √5-2i = (√3 + √5) + (i - 2i) = (√3 + √5) - i
What is the area of the triangle?
9 4 12
Answer:
13.636
Step-by-step explanation:
The area can be found using Heron's formula:
A = √(s(s-a)(s-b)(s-c))
where s=(a+b+c)/2.
For the given triangle, ...
a=9, b=4, c=12, s=(9+4+12)/2 = 12.5
A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636
The area of the triangle is about 13.636 square units.
Answer:
24 units\
Step-by-step explanation:
The amount of mites that survive a new cancer treatment can be modeled by Y = 25(0.5)x Determine which number represents the decayed rate
Answer:
Step-by-step explanation:
it is 0.5 since
y=25(0.5)x
since x is a variable that change usually describes the independent variable, and 25 is the sample that starts with, so 0.50 is the number that represent the decayed rates.
When circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%. Let X = the number of defective boards in a random sample of size, n = 25, so X∼Bin(25,0.05).
Required:
a. Determine P(X=3).
b. Determine P(X≤3).
c. Determine P(X≥4).
d. Determine P(1≤X≤3)..
e. What is the probability that none of the 25 boards is defective?
f. Calculate the expected value and standard deviation of X.
Answer:
(a) P(X=3) = 0.093
(b) P(X≤3) = 0.966
(c) P(X≥4) = 0.034
(d) P(1≤X≤3) = 0.688
(e) The probability that none of the 25 boards is defective is 0.277.
(f) The expected value and standard deviation of X is 1.25 and 1.089 respectively.
Step-by-step explanation:
We are given that when circuit boards used in the manufacture of compact disc players are tested, the long-run percentage of defectives is 5%.
Let X = the number of defective boards in a random sample of size, n = 25
So, X ∼ Bin(25,0.05)
The probability distribution for the binomial distribution is given by;
[tex]P(X=r)= \binom{n}{r} \times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,......[/tex]
where, n = number of trials (samples) taken = 25
r = number of success
p = probability of success which in our question is percentage
of defectivs, i.e. 5%
(a) P(X = 3) = [tex]\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}[/tex]
= [tex]2300 \times 0.05^{3}\times 0.95^{22}[/tex]
= 0.093
(b) P(X [tex]\leq[/tex] 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)
= [tex]\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}+\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}[/tex]
= [tex]1 \times 1 \times 0.95^{25}+25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}[/tex]
= 0.966
(c) P(X [tex]\geq[/tex] 4) = 1 - P(X < 4) = 1 - P(X [tex]\leq[/tex] 3)
= 1 - 0.966
= 0.034
(d) P(1 ≤ X ≤ 3) = P(X = 1) + P(X = 2) + P(X = 3)
= [tex]\binom{25}{1} \times 0.05^{1}\times (1-0.05)^{25-1}+\binom{25}{2} \times 0.05^{2}\times (1-0.05)^{25-2}+\binom{25}{3} \times 0.05^{3}\times (1-0.05)^{25-3}[/tex]
= [tex]25 \times 0.05^{1}\times 0.95^{24}+300 \times 0.05^{2}\times 0.95^{23}+2300 \times 0.05^{3}\times 0.95^{22}[/tex]
= 0.688
(e) The probability that none of the 25 boards is defective is given by = P(X = 0)
P(X = 0) = [tex]\binom{25}{0} \times 0.05^{0}\times (1-0.05)^{25-0}[/tex]
= [tex]1 \times 1\times 0.95^{25}[/tex]
= 0.277
(f) The expected value of X is given by;
E(X) = [tex]n \times p[/tex]
= [tex]25 \times 0.05[/tex] = 1.25
The standard deviation of X is given by;
S.D.(X) = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{25 \times 0.05 \times (1-0.05)}[/tex]
= 1.089
[PLEASE HURRY WILL GIVE BRAINLIEST] A square prism was sliced not perpendicular to its base and not through any of its vertices. What is the shape of the cross section shown in the figure?
It appears to be a parallelogram. But without actual numerical data, I don't think it's possible to prove this or not. I could be missing something though.
y = 3x + 4, what is y when x is 1, 2, and 3?
Answer:
When x is 1, y=7
When x is 2, y=10
When x is 3, y= 13
Step-by-step explanation: Plug in each number for x and solve
Answer:
If x=1, y=7
If x=2, y=10
If x=3, y=13
Step-by-step explanation:
For every equation substitute x in y = 3x + 4, with the value you want.
For example the first one says when x=1, so simply substitute x with 1 in y = 3x + 4.
So it'll look something like this:
y = 3(1) + 4.
Simply solve the equation from there, and you'll get y=7, and we know that x is already equal to 1.
So if x=1, then y=7
