Answer:
y=2.4
Step-by-step explanation:
7y-2=2y+10
7y-2y=10+2
5y=12
y=12/5=2.4
Find the third-degree polynomial function that has zeros −2 and −15i, and a value of 1,170 when x=3.
Answer:
The third degree polynomial function = x³ + 27x² + 200x + 300
Step-by-step explanation:
The third-degree polynomial function has zeros −2 and −15.
From the above, we have been given two factors of the polynomial function. Let's derive the factors from the two zeros of the polynomial given.
The two given zeros of the polynomial can be written as:
x= -2
x+2 = 0
(x+2) is a factor of the polynomial
x= -15
x+15 = 0
(x+15) is a factor of the polynomial
So we have two factors of the polynomial (x+2) and (x+15). But since it is a third degree polynomial, we have to find the third factor.
Let (x-b) be the third factor and f(x) represent the third degree polynomial
f(x) = (x-b) (x+2) (x+15)
Expanding (x+2) (x+15) = x² + 2x + 15x + 30
(x+2) (x+15) = x² + 17x + 30
f(x) = (x-b) (x² + 17x + 30)
From the given information, a value of 1,170 is obtained when x=3
f(3) = 1170
Insert 3 for x in f(x)
f(3) = (3-b) (3² + 17(3) + 30)
1170 = (3-b) (9 + 51 + 30)
1170 = (3-b) (90)
1170/90 = 3-b
3-b = 13
b = 3-13 = -10
Insert value of b in f(x)
f(x) = [x-(-10)] (x² + 17x + 30)
f(x) = (x+10) (x² + 17x + 30)
f(x) = x³ + 17x² + 30x + 10x² + 170x + 200x + 300
f(x) = x³ + 27x² + 200x + 300
The third degree polynomial function = x³ + 27x² + 200x + 300
Which expression best represents the situation?
Select the expression that best matches the scenario.
O4 + x + 3
4(x + 3)
4.3
4x + 3
Tyson bought a burger for himself and
each of his 3 friends. He left a tip of $3.
Which expression could represent
the amount of money Tyson spent?
Explain your thinking.
Help plz
Answer:509
Step-by-step explanation:600
A thermometer shows a temperature of Negative 20 and three-fourths degrees. A chemist recorded this temperature in her notebook using a decimal. Which number did the chemist write in the notebook?
Answer:
20.75
Step-by-step explanation:
Answer:
C. -20.75
Step-by-step explanation:
A computer manufacturer conducted a survey. It showed that a younger customer will not necessarily purchase a lower or higher priced computer. What is likely true? There is no correlation between age and purchase price. There is a correlation between age and purchase price. There may or may not be causation. Further studies would have to be done to determine this. There is a correlation between age and purchase price. There is probably also causation. This is because there is likely a decrease in the purchase price with a decrease in age.
Answer:
There is no correlation between age and purchase price
Step-by-step explanation:
In the survey, the researcher found out that a younger customer will not necessarily purchase a lower or higher priced computer thing it is likely true that there might be no correlation between purchase price and age.
It assumes that a younger customer can buy either buy a lower priced computer or can also buy a higher priced if he or she has the money for it.
Are the two terms on each tile like terms? Sort the tiles into the appropriate categories.
-7y^2and y^2
-4p and p^2
0.5kt and -10kt
6 and 9
5x and 5
3ad and 2bd
Answer:
LIKE TERMS: 6 and 9, 0.5kt and -10kt, and -7y2 and y2. UNLIKE TERMS: 3ad and 2bd, 5x and 5, and the last one is -4p and p2
Step-by-step explanation:
Answer: like terms: 6&9 , 0.5kt&-10kt , -7y^2&y^2
unlike terms 3ad&2bd, 5x&5, -4p&p^2
Step-by-step explanation:
passed
Find the characteristic polynomial and the eigenvalues of the matrix. [Start 2 By 2 Matrix 1st Row 1st Column 11 2nd Column 2 2nd Row 1st Column 2 2nd Column 11 EndMatrix ]The characteristic polynomial is nothing.
Answer:
Step-by-step explanation:
The answer is 3x 987 colunm 2
What’s the correct answer for this?
Answer:
s = 4.43
Step-by-step explanation:
Using formula for bigger circle
s =r∅
Where s is the Arc length, r is rdius and ∅ is theta(angle)
8.84=5∅
∅= 8.84/5
Angle = 1.77 radians
So both angles equal to 1.77 radians
Now again
Using formula
s = r∅
Where s is the Arc length, r is rdius and ∅ is theta(angle)
s = (2.5)(1.77)
s ≈ 4.43
Please help! Correct answer only, please! Consider the matrix shown below: Find the determinant of the matrix Q. A. -67 B. -65 C. 65 D. 67
Answer: d) 67
Step-by-step explanation:
[tex]determinant\ \left[\begin{array}{ccc}a&b&c\\d&e&f\\g&h&j\end{array}\right] = a\cdot det\left[\begin{array}{cc}e&f\\h&j\end{array}\right] -\ b\cdot det\left[\begin{array}{cc}d&f\\g&j\end{array}\right] +\ c\cdot det\left[\begin{array}{cc}d&e\\g&h\end{array}\right][/tex]
[tex]determinant\ \left[\begin{array}{ccc}2&3&4\\-3&2&1\\5&-1&6\end{array}\right] \\\\\\= 2\cdot det\left[\begin{array}{cc}2&1\\-1&6\end{array}\right] -\ 3\cdot det\left[\begin{array}{cc}-3&1\\5&6\end{array}\right] +\ 4\cdot det\left[\begin{array}{cc}-3&2\\5&-1\end{array}\right]\\\\\\=2[2(6)-1(-1)]-3[-3(6)-1(5)]+4[3(-1)-2(5)]\\\\\\=2(13)-3(-23)+4(-7)\\\\\\=26+69-28\\\\\\=\large\boxed{67}[/tex]
Graph the equation below by plotting the
y-intercept and a second point on the
line.
Answer:
Step-by-step explanation:
On the y-axis, graph the point on (0,4). Then from there, go up one, and to the right 4.
The base of a rectangular prism has an area of 24 square millimeters. The volume of the prism is 144 cubic millimeters. The shape is a cube. What is the height of the prism?
Answer:
height = 6 mm
Step-by-step explanation:
The prism is a rectangular prism. The base area of the prism is 24 mm². The volume of the prism is given as 144 mm³.
The height of the prism can be solved as follows.
Volume of the rectangular prism = Bh
where
B = base area
h = height
Volume = 144 mm³
B = 24 mm²
volume = Bh
144 = 24 × h
144 = 24h
divide both sides by 24
h = 144/24
h = 6 mm
Answer:
c
Step-by-step explanation:
edg 2022
A bottler of drinking water fills plastic bottles with a mean volume of 1,007 milliliters (mL) and standard deviation The fill volumes are normally distributed. What proportion of bottles have volumes less than 1,007 mL?
Answer:
0.5 = 50% of bottles have volumes less than 1,007 mL
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 1007[/tex]
What proportion of bottles have volumes less than 1,007 mL?
This is the pvalue of Z when X = 1007. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{1007 - 1007}{\sigma}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5
0.5 = 50% of bottles have volumes less than 1,007 mL
the sum of the three numbers in 2003,two of the numbers are 814 and 519 what is the third number
Answer:
670
Step-by-step explanation:
2003-814=1189
1189-519=670
Answer: The third number is 670.
Step-by-step explanation:
The sum means three numbers being added up is equal to 2003 so give two of those numbers you have to add them up and subtract it from 2003 to find the third number.
814 + 519 + x = 2003 where x is the third number
1333 + x = 2003
-1333 -1333
x = 670 So the third number is 670
Check:
814 + 670 + 519 = 2003
2003 = 2003 so yes again 670 is the third number.
Let D= {(x,y) | x^2+y^2 ≤ 4x} Using polar coordinates, What is the integral: ∬y^2/ (x^2+y^2)dxdy?
In polar coordinates, the inequality changes to
[tex]x^2+y^2\le4x\implies r^2\le4r\cos\theta\implies r\le4\cos\theta[/tex]
which is a circle of radius 2 and centered at (2, 0). The set D is then
[tex]D=\left\{(r,\theta)\mid0\le r\le4\cos\theta\land0\le\theta\le\pi\right\}[/tex]
The integral is then
[tex]\displaystyle\iint_D\frac{y^2}{x^2+y^2}\,\mathrm dx\,\mathrm dy=\int_0^\pi\int_0^{4\cos\theta}\frac{r^2\sin^2\theta}{r^2}r\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\int_0^\pi\int_0^{4\cos\theta}r\sin^2\theta\,\mathrm dr\,\mathrm d\theta[/tex]
[tex]=\displaystyle\frac12\int_0^\pi((4\cos\theta)^2-0^2)\sin^2\theta\,\mathrm d\theta[/tex]
[tex]=\displaystyle8\int_0^\pi\cos^2\theta\sin^2\theta\,\mathrm d\theta[/tex]
There are several ways to compute the remaining integral; one would be to invoke the double-angle formula,
[tex]\sin(2\theta)=2\sin\theta\cos\theta[/tex]
so that the integral is
[tex]=\displaystyle8\int_0^\pi\frac{\sin^2(2\theta)}4\,\mathrm d\theta[/tex]
[tex]=\displaystyle2\int_0^\pi\sin^2(2\theta)\,\mathrm d\theta[/tex]
Then invoke another double-angle formula,
[tex]\sin^2\theta=\dfrac{1-\cos(2\theta)}2[/tex]
to change the integral to
[tex]=\displaystyle\int_0^\pi1-\cos(4\theta)\,\mathrm d\theta[/tex]
[tex]=(\pi-\cos(4\pi))-(0-\cos0)=\boxed{\pi}[/tex]
Mary is three quarters of Cameron's age. Mary is 24 years old. How old is Cameron?
Answer:
32 years oldStep-by-step explanation:
3/4=24 so 1/4= 24÷3= 8
1/4=8
So to get 4/4 or Cameron's age it is 8×4=32yrs
[tex]answer \\ 32 \: years \: old \\ solution \\ mary's \: age = 24 \\ let \: cameron's \: age \: be \: x \\ given \\ \frac{3}{4} x = 24 \\ or \: x = 24 \times \frac{4}{3} \\ x = 32 \\ hope \: it \: helps[/tex]
What’s the correct answer for this?
Answer:
E:
Step-by-step explanation:
The equation of circles is
(x-a)²+(y-b)²=r²
Where
Center = (a,b) = (-6,-3) and r = 12
Now
The equation becomes
(x+6)²+(x+3)²=144
a consumer affairs company is interested in testing at the 5% level of significance that the average weight of a package of butter is less than 16 oz if the p value is 0.003 the conclusion is
Which value of a in the exponential function below would cause the function to shrink? f(x) = a(three-halves) Superscript x Four-fifths Five-fourths Three-halves Seven-fourths
Answer:
Four-fifths
Step-by-step explanation:
As we know that
By multiplying the function by a constant, we may expand or shrink the function in the y-direction.
Now we have
[tex]y=a(b^{x})[/tex]
if [tex]a> 1[/tex] > the function would enlarge
if [tex]0< a < 1[/tex] > the function would shrinks
Now
For case A
[tex]a = \frac{4}{5}[/tex]
[tex]0 < (\frac{4}{5} )< 1[/tex] ....... > the function would shrinks
For case B
[tex]a = \frac{5}{4}[/tex]
[tex](\frac{5}{4} )>1[/tex] .......> the function would enlarge
For case C
[tex]a = \frac{3}{2}[/tex]
[tex](\frac{3}{2} )>1[/tex] .........> the function would enlarge
For case D
[tex]a = \frac{7}{4}[/tex]
[tex](\frac{7}{4} )>1[/tex] .........> the function would enlarge
Therefore the second option is correct
Answer: 4/5
Step-by-step explanation: E2020
please answer this correctly
Answer:
557
Step-by-step explanation:
l x w
13x24
13x7
22x7
557
A comparison is made between two bus lines to determine if arrival times of their regular buses from Denver to Durango are off schedule by the same amount of time. For 51 randomly selected runs, bus line A was observed to be off schedule an average time of 53 minutes, with standard deviation 17 minutes. For 60 randomly selected runs, bus line B was observed to be off schedule an average of 60 minutes, with standard deviation 13 minutes. Do the data indicate a significant difference in average off-schedule times? Use a 5% level of significance.
a. Level of significance, null and alternative hypothesis
b. What sampling distribution will you use? What assumptions are you making? What is the value of the sample test statistic?
c. Find or estimate the P-value
d. Based on your answers to part a and c will you reject or fail to reject the null hypothesis? Are the data statistically significant at level alpha?
e. Interpret your conclusion in the context of the application
Answer:
a) Level of significance α=0.05
Two-tailed test, with null and alternative hypothesis:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
b) Student's t distribution. We assume equal variances for both populations, independent sampled values and populations normally distributed.
Test statistic t=-2.4
c) P-value = 0.018
d) Rejection of the null hypothesis.
The data is statistically significant.
e) There is evidence to conclude there is significant difference in average off-schedule times between the bus lines. The difference we see in the samples seems not due to pure chance.
Step-by-step explanation:
This is a hypothesis test for the difference between populations means.
The claim is that there is a significant difference in average off-schedule times for this bus lines.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0[/tex]
The significance level is 0.05.
The sample 1 (bus line A), of size n1=51 has a mean of 53 and a standard deviation of 17.
The sample 2 (bus line B), of size n2=60 has a mean of 60 and a standard deviation of 13.
The difference between sample means is Md=-7.
[tex]M_d=M_1-M_2=53-60=-7[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{17^2}{51}+\dfrac{13^2}{60}}\\\\\\s_{M_d}=\sqrt{5.667+2.817}=\sqrt{8.483}=2.913[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-7-0}{2.913}=\dfrac{-7}{2.913}=-2.4[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=51+60-2=109[/tex]
This test is a two-tailed test, with 109 degrees of freedom and t=-2.4, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-2.4)=0.018[/tex]
As the P-value (0.018) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there is a significant difference in average off-schedule times for this bus lines.
–3y = 15 – 4x rewritten in slope-intercept form is
Answer:
[tex] y = \frac{4}{3} - 5[/tex]
Step-by-step explanation:
[tex] - 3y = 15 - 4x \\ - 3y = - 4x + 15 \\ \\ y = \frac{ - 4x + 15}{ - 3} \\ \\ y = \frac{ - 4}{ - 3} x + \frac{15}{ - 3} \\ \\ y = \frac{4}{3} x - 5 \\ which \: is \: in \: slope - intercept \: form.[/tex]
please see attachment
Answer:
a) The value of absolute minimum value = - 0.3536
b) which is attained at [tex]x = \frac{1}{\sqrt{2} }[/tex]
Step-by-step explanation:
Step(i):-
Given function
[tex]f(x) = \frac{-x}{2x^{2} +1}[/tex] ...(i)
Differentiating equation (i) with respective to 'x'
[tex]f^{l} = \frac{2x^{2} +1(-1) - (-x) (4x)}{(2x^{2}+1)^{2} }[/tex] ...(ii)
[tex]f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} }[/tex]
Equating Zero
[tex]f^{l}(x) = \frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0[/tex]
[tex]\frac{2x^{2}-1}{(2x^{2}+1)^{2} } = 0[/tex]
[tex]2 x^{2}-1 = 0[/tex]
[tex]2 x^{2} = 1[/tex]
[tex]x^{2} = \frac{1}{2}[/tex]
[tex]x = \frac{-1}{\sqrt{2} } , x = \frac{1}{\sqrt{2} }[/tex]
Step(ii):-
Again Differentiating equation (ii) with respective to 'x'
[tex]f^{ll}(x) = \frac{(2x^{2} +1)^{2} (4x) - 2(2x^{2} +1) (4x)(2x^{2}-1) }{(2x^{2}+1)^{4} }[/tex]
put
[tex]x = \frac{1}{\sqrt{2} }[/tex]
[tex]f^{ll} (x) > 0[/tex]
The absolute minimum value at [tex]x = \frac{1}{\sqrt{2} }[/tex]
Step(iii):-
The value of absolute minimum value
[tex]f(x) = \frac{-x}{2x^{2} +1}[/tex]
[tex]f(\frac{1}{\sqrt{2} } ) = \frac{-\frac{1}{\sqrt{2} } }{2(\frac{1}{\sqrt{2} } )^{2} +1}[/tex]
on calculation we get
The value of absolute minimum value = - 0.3536
Final answer:-
a) The value of absolute minimum value = - 0.3536
b) which is attained at [tex]x = \frac{1}{\sqrt{2} }[/tex]
What is the slope intercept form.
Answer:
y = 1/4x + 2
Step-by-step explanation:
Since they gave you point slope form already, all you need to do is convert that into slope-intercept form. Just distribute the parenthesis and move the 4 over. Once you do so, you should get C/3rd option as your answer.
Based on historical data, your manager believes that 39% of the company's orders come from first-time customers. A random sample of 171 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.21 and 0.32
Answer:
[tex] z= \frac{0.21- 0.39}{0.0373}= -4.829[/tex]
[tex] z= \frac{0.32- 0.39}{0.0373}=-1.877[/tex]
And we can find the probability with this difference:
[tex] P(-4.829<z< -1.877) = P(Z<-1.877) -P(Z<-4.829)=0.0303- 6.86x10^{-7}=0.0303[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex] n = 171[/tex] represent the sample size
[tex]p =0.39[/tex] the proportion of interest
We want to find the following probability:
[tex] P( 0.21 < \hat p < 0.32)[/tex]
We can use the normal approximation for this case since np >10 and n (1-p) >10
For this case we know that the distribution for the sample proportion is given by:
[tex]\hat p \sim N( p , \sqrt{\frac{p (1-p)}{n}} )[/tex]
And we can use the following parameters:
[tex] \mu_{\hat p}= 0.39[/tex]
[tex] \sigma_{\hat p} =\sqrt{\frac{0.39*(1-0.39)}{171}}= 0.0373[/tex]
And we can apply the z score formula given by:
[tex] z = \frac{p \\mu_{\hat p}}{\sigma_{\hat p}}[/tex]
And using this formula we got:
[tex] z= \frac{0.21- 0.39}{0.0373}= -4.829[/tex]
[tex] z= \frac{0.32- 0.39}{0.0373}=-1.877[/tex]
And we can find the probability with this difference:
[tex] P(-4.829<z< -1.877) = P(Z<-1.877) -P(Z<-4.829)=0.0303- 6.86x10^{-7}=0.0303[/tex]
what is the diagonal of asquare with length 3cm
Answer:
3√2
Step-by-step explanation:
If you draw the diagonal, you have a 45°45°90° triangle.
The two legs are 3, so the hypotenuse is 3√2
The table below represents the total cost of leasing a car at the end each month.
Month 1 -------- 3 -------- 8 -------- 12
Cost $1,859 --- $2,577 --- $4,372 --- $5,808
Write an equation in slope-intercept form to represent the total cost, y, of leasing a car for x months.
Answer:
y= 359 x+1500
Step-by-step explanation:
find the slope m= (2577-1859)÷(3-1) = 359
y=mx+b
find b : substitute x ,y, and m
get b = 1857 - 359*1 = 1500
Answer:
y= 359 x+1500
Step-by-step explanation:
Find the area of a regular hexagon with a side length of 5cm, Round to the nearest tenth.
Answer:
i think its 64.95cm
Step-by-step explanation:
Peter has invented a game with paper cups. He lines up 121 cups face down in a straight line from left to right and consecutively labels them from 1 to 121. He then walks from left to right down the line of cups, flipping all of the cups over. He returns to the left end of the line, then makes a second pass from left to right, this time flipping cups 2,4,6,8... On the third pass, he flips cups 3,6,9,12.... He continues like this: On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.) After 121 passes, how many cups are face up?
Answer:
After 121 passes, there will be 11 cups facing up
Step-by-step explanation:
Given that:
Peter initially lines up 121 cups facing down in a straight line from left to right and consecutively labels them from 1 to 121.
We can have an inequality ; i.e 1 ≤ n ≤ 121; if n represents the divisor including n itself for which n = odd number. Thus at the end of this claim, the cup will be facing up.
On the ith pass, he flips over cups i, 2i, 3i, 4i,.... (By "flip," we mean changing the cup from face down to face up or vice versa.)
For each divisor on the ith pass of n;
[tex]i \ th \ pass \ = \ n \ \to \ p |n[/tex] since we are dealing with possibility of having an odds number:
Thus; [tex]p =i[/tex] and [tex]i^2 = n[/tex] where ; n = perfect square.
Thus ; we will realize that between 1 to 121 ; there exist 11 perfect squares. Therefore; as a result of that ; 11 cups will definitely be facing up after 121 passes
A square has an area of 349.69m2.
Work out the perimeter of the square.
Answer:
[tex]74.8m[/tex]
Step-by-step explanation:
[tex]A=a^2\\P=4a\\P=4\sqrt{A} \\=4*\sqrt{349.69} \\=74.8m[/tex]
1. Ryan budgets $35 a week for lunch for 5 days. What
is his average lunch expense each day?
Answer: $7
Step-by-step explanation:
35/ 5 = 7
Answer:
$7
Step-by-step explanation:
Bc/ 35/5=7
Help asap giving branlist!!!
Answer:
Option A.
The heartbeat has a pattern of 60 + (5 x minutes) and linear graphs are straight. The only way the linear graph is straight if there is a pattern.
Step-by-step explanation:
