Which of these numbers is prime? 13, 30, 49, 65, 87

Answer:

The answer is explained below

Step-by-step explanation:

Given that, the equation H*x = c is inconsistent for some c in R^n, we can say that the equation A*x = b has at least one solution for each b in R^n of IMT (Inverse Matrix Theorem) is not fulfilled.

Thanks to this we can say that by equivalence of theorem statement, the equation H*x = 0 will not have only the trivial solution. It will have non-trivial solutions too.

Answer:

the 3rd option is the answer

Step-by-step explanation:

I hope the attached file is self-explanatory

Answer:

41

Step-by-step explanation:

If Skylar has 4 times as many books as Karen, that means that you have to do a division problem to figure out how books Karen has. Because Skylar has 4 times as many books, and she has 164 books, the division problem is 164÷4=41 books.

The number of books Karen has will be 41.

Simplifying means making something easier to do or comprehend, as well as making something less difficult.

Let,

Skylar has x number of books

Karen has y number of books = 164

Given condition;

y=4x

164=4x

x=41 books

Hence Karen has 41 books.

To learn more about the simplification, refer to:

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Answer:

[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]    

[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]    

And the confidence interval would be given by (2137, 2203)

Step-by-step explanation:

2051 ,2061 ,2162 ,2167 , 2169 ,2171 , 2180 , 2183 , 2186 , 2195 , 2196 , 2198 , 2205 , 2210  ,2211

We can calculate the mean and deviation with these formulas:

[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)  

[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)  

And we got:

[tex]\bar X=2169.67[/tex] represent the sample mean for the sample  

[tex]\mu[/tex] population mean

s=48.72 represent the sample standard deviation

n=15 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom are given by:

[tex]df=n-1=15-1=14[/tex]

Since the Confidence is 0.98 or 98%, the significance is [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.01[/tex], and using excel we calculate the critical value [tex]t_{\alpha/2}=2.624[/tex]

Now we have everything in order to replace into formula (1):

[tex]2169.67-2.624\frac{48.72}{\sqrt{15}}=2136.66[/tex]    

[tex]2169.67+2.624\frac{48.72}{\sqrt{15}}=2202.68[/tex]    

And the confidence interval would be given by (2137, 2203)

Steps to solve:

9(d - 93) = -36d

~Distribute

9d - 837 = -36d

~Subtract 9d to both sides

-837 = -45d

~Divide -45 to both sides

18.6 = d

Best of Luck!

Answer:

Height at t = 1 sec is 1144 ft

Step-by-step explanation:

Given:

Initial height of object = 1160 feet

Height of object after t seconds is given by the polynomial:

[tex]- 16t ^2+ 1160[/tex]

Let [tex]h(t)=- 16t ^2+ 1160[/tex]

Let us analyze the given equation once.

[tex]t^2[/tex] will always be positive.

and coefficient of [tex]t^2[/tex] is [tex]-16[/tex] i.e. negative value.

It means something is subtracted from 1160 ft (i.e. the initial height).

So, height will keep on decreasing with increasing value of t.

Also, given that the object is dropped from the top of a tower.

To find:

Height of object at t = 1 sec.

OR

[tex]h (1)[/tex] = ?

Solution:

Let us put t = 1 in the given equation: [tex]h(t)=- 16t ^2+ 1160[/tex]

[tex]h(1)=- 16\times 1 ^2+ 1160\\\Rightarrow h(1) = -16 + 1160\\\Rightarrow h(1) = 1144\ ft[/tex]

So, height of object at t = 1 sec is 1144 ft.

Answer:

1. y² - 3x - 18

2. 4x² - 33x + 35

3. 12x² - 11x + 2

Step-by-step explanation:

All we do with these questions are expanding the factored binomials. Use FOIL:

1. y² + 3y - 6y - 18

y² - 3y - 18

2. 4x² - 28x - 5x + 35

4x² - 33x + 35

3. 12x² - 3x - 8x + 2

12x² - 11x + 2

Answer:

1) (y-6) (y+3)

=> [tex]y^2+3y-6y-18[/tex]

=> [tex]y^2-3y-18[/tex]

2) (4x-5) (x-7)

=> [tex]4x^2-28x-5x+35[/tex]

=> [tex]4x^2-33x+35[/tex]

3) (3x - 2) ( 4x - 1)

=> [tex]12x^2-3x-8x+3[/tex]

=> [tex]12x^2-11x+3[/tex]

Answer:

4

Step-by-step explanation:

1, 3, 4, 6, 2, 4, 5, 6, 2, 3, 1, 4, 0, 4, 4, 4, 8, 9, 7, 4

Arrange the numbers from smallest to largest

0,1, 1,2,2, 3,3, 4, 4,4,4,4,4 , 4, 5, 6, 6,   7, 8, 9,

There are 20 numbers

The middle number is between 10 and 11

0,1, 1,2,2, 3,3, 4, 4,4   ,4,4,4 , 4, 5, 6, 6,   7, 8, 9,

The median is 4

Solution,

Arranging the data in ascending order:

0,1,1,2,2,3,3,4,4,4,4,4,4,4,5,6,6,7,8,9

N(total number of items)= 20

Now,

Median:

[tex] (\frac{n + 1}{2)} ) ^{th \: item} \\ = (\frac{20 + 1}{2} ) ^{th \: item} \\ = \frac{21}{2} \\ = 10.5 \: th \: \: item[/tex]

Again,

Median:

[tex] \frac{10 \: th \: item + 11 \: th \: item}{2} \\ = \frac{4 + 4}{2} \\ = \frac{8}{2} \\ = 4[/tex]

Given:

An equilateral triangle JKL inscribed in circle M.

Solution:

To draw an equilateral triangle inscribed in circle follow the steps:

1: Draw a circle with any radius.

2. Take any point A, anywhere on the circumference of the circle.

3.  Place the compass on point A, and swing a small arc crossing the circumference of the circle.

Remember the span of the compass should be the same as the radius of the circle.

4. Place the compass at the intersection of the previous arc and the circumference and draw another arc but don't change the span of the compass.

5. Repeat this process until you return to point A.

6. Join the intersecting points on the circle to form the equilateral triangle.

So the correct option is A. The width must be equal to the radius of circle M.

Answer:

x = 15

y = 90

Step-by-step explanation:

Step 1: Find x

We use Definition of Supplementary Angles

9x + 3x = 180

12x = 180

x = 15

Step 2: Find y

All angles in a triangle add up to 180°

3(15) + 3(15) + y = 180

45 + 45 + y = 180

90 + y = 180

y = 90°

Answer:

option D 9x³

Step-by-step explanation:

the monomial 9x³ comes from (3x)³, which gives, 3×3×3×x×x×x= 9x³

9 is 3 times 3 and x³ is 3 times x. So here, 9x³ is a perfect cube

Answer:

TRUE

Step-by-step explanation:

The circumcenter of a triangle is the center of the only circle that can be circumscribed about it

Answer:

False

Step-by-step explanation:

Answer: 151

Step-by-step explanation:

if prior population proportion is unknown , then the formula is used to find the sample size :

[tex]n=0.25(\frac{z_{\alpha/2}}{E})^2[/tex]

, where [tex]z_{\alpha/2}[/tex] = Two tailed critical value for significance level of [tex]\alpha.[/tex]

E = Margin of error.

Given : margin of error = 8%= .08

For 95% confidence level , two tailed critical value = 1.96

Now, the required sample size :

[tex]n=0.25(\frac{1.96}{0.08})^2\\\\=0.25(24.5)^2\\\\=150.0625\approx151[/tex]

Hence, the size of the sample needed = 151.

Answer:

a. The volume of Pyramid A is double that of Pyramid B.

b. The new volume of B is equal to the volume of A.

Step-by-step explanation:

The base of pyramid A is a rectangle with length 10 meters and width 20 meters.

The base of pyramid B is a square of side length 10 meter.

Both pyramids have the same height, h.

The volume of a pyramid is given as:

V = lwh / 3

where l = length

w = width

h = height

The volume of Pyramid A is:

V = (10 * 20 * h) / 3 = 66.7h cubic metres

The volume of Pyramid B is:

V = (10 * 10 * h) / 3 = 33.3h cubic metres

By comparing their values, the volume of Pyramid A is double that of Pyramid B.

If the height of B increases to 2h, its new volume is:

V = (10 * 10 * 2h) / 3 = 66.7h cubic metres

The new volume of B is equal to the volume of A.

Answer:

  $904,510.28

Step-by-step explanation:

If we assume the withdrawals are at the beginning of the month, we can use the annuity-due formula.

  P = A(1 +r/n)(1 -(1 +r/n)^(-nt))/(r/n)

where r is the APR, n is the number of times interest is compounded per year (12), A is the amount withdrawn, and t is the number of years.

Filling in your values, we have ...

  P = $4000(1 +.034/12)(1 -(1 +.034/12)^(-12·30))/(.034/12)

  P = $904,510.28

You need to have $904,510.28 in your account when you begin withdrawals.

Answer:

You need to have $904,510.28 in your account when you begin

Answer:

The integers are 7 and 14.

Step-by-step explanation:

y = 2x

1/y + 1/x = 3/14

1/(2x) + 1/x 3/14

1/(2x) + 2/(2x) = 3/14

3/(2x) = 3/14

1/2x = 1/14

2x = 14

x = 7

y = 2x = 2(7) = 14

Answer: The integers are 7 and 14.

The required two integers are 7 and 14

This is a question on word problems leading to the simultaneous equation:

Let the two unknown integers be x and y. If a positive integer is twice another, then x = 2y .......... 1

Also, if the sum of the reciprocals of the two positive integers is 3/14, then:

[tex]\frac{1}{x}+ \frac{1}{y} =\frac{3}{14}[/tex] ..........2

Substitute equation 1 into 2

[tex]\frac{1}{2y} +\frac{1}{y} =\frac{3}{14} \\[/tex]

Find the LCM of 2y and y

[tex]\frac{1+2}{2y} =\frac{3}{14} \\\frac{3}{2y} =\frac{3}{14} \\\\cross \ multiply\\2y \times 3=3 \times 14\\6y=42\\y=\frac{42}{6}\\y=7[/tex]

Substitute y = 7 into equation 1:

Recall that x = 2y

[tex]x = 2(7)\\x = 14[/tex]

Hence the required two integers are 7 and 14.

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Answer:

2699

Step-by-step explanation:

you do all the multiplication first

500×6= 3000

5 ×50 = 250

so it becomes

3000-51-250 = 2699

Answer:

2699

Step-by-step explanation:

Answer:

[a] y=x^2+3,  vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

[d] y= (1/2)x^2 - 5, vertex, V(0,-5)

Step-by-step explanation:

The vertex, V, of a quadratic can be found as follows:

1. find the x-coordinate, x0,  by completing the square

2. find the y-coordinate, y0, by substituting the x-value of the vertex.

[a] y=x^2+3,  vertex, V(0,3)

y=(x-0)^2 + 3

x0=0, y0=0^2+3=3

vertex, V(0,3)

[b] y=2x^2, vertex, V(0,0)

y=2(x-0)^2+0

x0 = 0, y0=0^2 + 0 = 0

vertex, V(0,0)

[c] y=-x^2 +  4, vertex, V(0,4)

y=-(x^2-0)^2 + 4

x0 = 0, y0 = 0^2 + 4 = 4

vertex, V(0,4)

y = (1/2)(x-0)^2 -5

x0 = 0, y0=(1/2)0^2 -5 = -5

vertex, V(0,-5)

Conclusion:

When the linear term (term in x) is absent, the vertex is at (0,k)

where k is the constant term.

Answer:

B

Step-by-step explanation:

The answer is B because in order for the square root of a number to be equal to another number, the answer squared should be the number under the square root.

B. [tex](-4)^2\neq -16[/tex].

Hope this helps.

Answer:

3/10

Step-by-step explanation:

We have that the Armans last winter had 5/6 of a row of stacked logs and at the end of the winter he had 8/15 of the same row left, therefore:

Ambitious

First we have to do is that the denominator is the same.

in the case of 5/6 it would be 25/30

and for 8/15 it would be 16/30

Now if we can do the subtraction and it would be:

25/30 - 16/30 = 9/30 or what equals 3/10

3/10 was the amount of wood he burned in the winter

Answer:

D) 3/10 row

Step-by-step explanation:

Answer:

A velocity of 120km/h is needed to cover the distance in one hour

Step-by-step explanation:

The velocity formula is:

[tex]v = \frac{d}{t}[/tex]

In which v is the velocity, d is the distance and t is the time.

A car travelling from Ibadan to Lagos at 90 km/hr takes 1 hour 20 min.

This means that [tex]v = 90, t = 1 + \frac{20}{60} = 1.3333[/tex]

We use this to find d.

[tex]v = \frac{d}{t}[/tex]

[tex]90 = \frac{d}{1.3333}[/tex]

[tex]d = 90*1.3333[/tex]

[tex]d = 120[/tex]

The distance is 120 km.

How fast must one travel to cover the distance in one hour?

Velocity for a distance of 120 km(d = 120) in 1 hour(t = 1). So

[tex]v = \frac{d}{t}[/tex]

[tex]v = \frac{120}{1}[/tex]

[tex]v = 120[/tex]

A velocity of 120km/h is needed to cover the distance in one hour

Answer:

The better deal would be simple interest rate of 3.2%

Step-by-step explanation:

In order to calculate which bank would be the better deal If Parker decides to deposit $7,000 for 25 years, we would have to make the following calculation:

A. simple interest rate of 3.2%.

Therefore, FV= P*r*t

=$7,000*3.2%*25

=$5,600.

B. compound interest rate of 3%

Therefore, FV=PV(1+r)∧n

FV=$7,000(1+0.03)∧25

FV=$14,656

The better deal would be simple interest rate of 3.2%

━━━━━━━☆☆━━━━━━━

▹ Answer

V ≈ 160.22

▹ Step-by-Step Explanation

V = πr²[tex]\frac{h}{3}[/tex]

V = π3²[tex]\frac{17}{3}[/tex]

V ≈ 160.22

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

[tex]\huge\boxed{x=\sqrt{66}}[/tex]

Step-by-step explanation:

ΔADC and ΔABD are similar (AAA)

Therefore the cooresponging sides are in proportion:

[tex]\dfrac{AD}{AC}=\dfrac{AB}{AD}[/tex]

Substitute

[tex]AD=x;\ AC=6+5=11;\ AB=6[/tex]

[tex]\dfrac{x}{11}=\dfrac{6}{x}[/tex]          cross multiply

[tex](x)(x)=(11)(6)\\\\x^2=66\to x=\sqrt{66}[/tex]

Answer:

2/7

Step-by-step explanation:

The numbers greater than 7 or less than 3 are 2 and 8.

2 numbers out of 7.

P(greater than 7 or less than 3) = 2/7

Answer:

2/7

Step-by-step explanation:

There are a total of 7 sample spaces also known as 2,3,4,5,6,7,8. Now we have to find a number greater than 7 and less than 3. 2 is less than 3, and 8 is greater than 7, so two numbers are selected. This would become 2/7 because out of all of the 7 outcomes, only two are selected.

Answer: (3y - 10)*2÷4

Step-by-step explanation:

Because 10 less than 3 times a number, y, is done first, it is in parenthesis.  The 3 is there to represent the "three times" and the -10 is there to represent the "ten less".  The *2 is there to represent the "multiplied by two" and the ÷4 is there to represent the "divided by 4"

Hope it helps, and tyvm <3

Answer:

[tex]\displaystyle \frac{2(3y - 10)}{4}[/tex]

Step-by-step explanation:

10 less than 3 times y.

The variable y is multiplied by 3, 10 is subtracted from 3 × y.

The result 3y - 10 is then multiplied by 2.

2(3y - 10) is then divided by 4.

Answer: The lines are skew.

Step-by-step explanation: Two lines can only be parallel OR skew Or intersect each other. To determine that:

1) If the lines are parallel, divide the coefficient that precedes the variable of each equation and compare:

[tex]\frac{7}{8} \neq \frac{6}{8} \neq \frac{1}{4}[/tex]

Since they are not equal, L1 and L2 are not parallel.

2) If the lines intersect, when you equal the equations the variable is a valid statement:

25 + 7t = - 12 + 8t (1)

17 + 6t = - 17 + 8t (2)

t = - 11 + 4t (3)

Using (3) to solve the system:

t - 4t = - 11

3t = 11

t = [tex]\frac{11}{3}[/tex]

Substituing t in (1):

25 + 7(11/3) = -12 + 8(11/3)

25 + 77/3 = - 12 + 88/3

[tex]\frac{152}{3} = \frac{52}{3}[/tex]

Which is not true, so, the lines does NOT intersect.

As they are none of the other options, it can be concluded that the lines L1 and L2 are skew.

Answer:

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

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].

For this problem, we have that:

[tex]n = 2305, \pi = \frac{339}{2305} = 0.147[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 - 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.133[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.147 + 1.96\sqrt{\frac{0.147*0.853}{2305}} = 0.161[/tex]

The 95% confidence interval for the proportion of college students who get 8 or more hours of sleep per night is (0.133, 0.161).

Answer:

multiply 0.85x40

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

This problem can be solved using angular bisector theorem.

It states that if any angle of triangle is bisected by a line , then that line

divides the opposite side of that angle in same proportion as that of two other sides which contain the angle.

__________________________________

Here one angle is is divided into parts theta

Thus,

using angular bisector theorem

14/21 = 6/3x-12

=> 14(3x-12) = 21*6

=> 3x-12 = 21*6/14 = 9

=> 3x = 12+9 = 21

=> x = 21/3 = 7

Thus, x = 7