Solve the system by the method of substitution.

1.5x + 0.8y = 2.3
0.3x − 0.2y = 0.1

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:

Explained below.

Step-by-step explanation:

The question is:

Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice.

Set A: {36, 51, 37, 42, 54, 39, 53, 42, 46, 38, 50, 47}

Set B: {22, 57, 46, 24, 31, 41, 64, 50, 28, 59, 65, 38}

The five-number summary is:

The five-number summary for set A is:

Variable   Minimum       Q₁         Median        Q₃         Maximum

  Set A       36.00       38.25        44.00       50.75        54.00

The five-number summary for set B is:

Variable   Minimum       Q₁         Median        Q₃         Maximum

 Set B         22.00      28.75        48.00       58.50         65.00

Compute the mean for both the data as follows:

[tex]Mean_{A}=\frac{1}{12}\times [36+51+37+...+47]=44.58\approx 44.6\\\\Mean_{B}=\frac{1}{12}\times [22+57+46+...+38]=44.58\approx 44.6[/tex]

Compare mean and median for the two data:

[tex]Mean_{A}>Median_{A}\\\\Mean_{B}>Median_{B}[/tex]

Compute the standard deviation for both the set as follows:

[tex]SD_{A}=\sqrt{\frac{1}{12-1}\times [(36-44.6)^{2}+...+(47-44.6)^{2}]}=6.44\approx 6.4\\\\SD_{B}=\sqrt{\frac{1}{12-1}\times [(22-44.6)^{2}+...+(38-44.6)^{2}]}=15.56\approx 15.6[/tex]

Answer:

2.99

Step-by-step explanation:

Take the total cost and divide by the number of cards

71.76/24 = 2.99

The cost per car is 2.99

Answer:

b. $2.99.

Step-by-step explanation:

To get the price per car, you get the total price divided by the total number of cars.

That would be 71.26 / 24 = 2.969166667, which is most close to b. $2.99. Those are some cheap cars!

Hope this helps!

Answer:

x^2   +y^2 = 16    

Step-by-step explanation:

The equation of a circle is given by

(x-h) ^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the radius

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

x^2   +y^2 = 16        

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:

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:

[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:

  x -2y = -9

Step-by-step explanation:

We can start by swapping the coefficients of x and y, then negating one of them. We can finish by evaluating the expression at the given point to find the constant.

  2x -4y = constant

  2(1) -4(5) = -18 = constant

So, an equation could be ...

  2x -4y = -18

We notice that all of the coefficients of this equation are divisible by 2, so we can remove a factor of 2 from the equation:

  x -2y = -9

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:

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:

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:

multiply 0.85x40

Step-by-step explanation:

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]

Answer:

-978

Step-by-step explanation:

1.) Use Distributive property (by multiplying 15 by the values in parentheses): -735=15m + 13935

2.) Subtract 13,935 on both sides, to move that value to the left side, to further  isolate the variable m.

-735-13935=15m + 13935 - 13935

3.)-Simplify/Combine Like Terms

-14,670=15m

4.) Divide both sides by 15 to isolate and solve for m

-14,670/15=15m/15

5.) Simplify

-978=m    

6.) Rearrange so m is on left side and value is on right side

m=-978

Answer:

D. No solution

Step-by-step explanation:

Instead of solving everything I just plugged the numbers on equations and saw that for some of them the numbers satisfied one or two equation but not all.  Also for some I saw that a number set makes the equation have no solution. For eg, I plugged option B into equation 3 and got 1305=756 which is never true so it is no solution.

Hope you understand :)

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:

The value of digit 5 is thousand

Step-by-step explanation:

Digit 5 has thousand value in 75 389

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:

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:

  $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 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:

I think so you meant to write 62 as 6^2

If this is the question , then the answer is 6 x 6

HOPE THIS HELPS AND PLS MARK AS BRAINLIEST

THNXX :)

Answer:

B. 6 × 6

Step-by-step explanation:

6²

The square of a number means that the number is multiplied by itself.

6 × 6 (expanded form)

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:

If the correlation coefficient is 1, then the slope must be 1 as well.

Step-by-step explanation:

Coefficient of correlation is used in statistics to determine the relationship between two variables. Correlation coefficient and slope always have same sign. It measures the strength of linear relation between two variables. The values of correlation coefficient ranges between 0 to 1. where 0 determines that there is no relationship between two variables.

If the correlation coefficient is 1, then the slope must be 1 as well.

The correlation coefficient (ρ) is a measure that determines the degree to which the movement of two different variables is associated.

So, the false statement is:

If the correlation coefficient is 1, then the slope must be 1 as well.

Learn more:https://brainly.com/question/16557696

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

Answer:

1

Hope that helps.

Answer:

1

Step-by-step explanation:

16/16=1

Hope this helps, if you have any questions, feel free to ask

Have a good day! :)

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:

[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)

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.