[tex] 3 {x}^{2} - 15x = 15[/tex]
​

Correct question:

The vector matrix [ [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex] is dilated by a factor of 1.5 and then reflected across the x axis. If the resulting matrix is [a/b] then a=??? and b=???

Answer:

a = 3

b = 10.5

Step-by-step explanation:

Given:

Vector matrix = [tex] \left[\begin{array}{ccc}2\\7\end{array}\right] [/tex]

Dilation factor = 1.5

Since the vector matrix is dilated by 1.5, we have:

[tex] \left[\begin{array}{ccc}1.5 * 2\\1.5 * 7\end{array}\right] [/tex]

= [tex] \left[\begin{array}{ccc}3\\10.5\end{array}\right] [/tex]

Here, we are told the vector is reflected on the x axis.

Therefore,

a = 3

b = 10.5

Answer:

a = 3

b = -10.5

Step-by-step explanation:

got a 100% on PLATO

An event that is impossible has a probability of 0

An event that is certain to happen has a probability of 1

The probability scales from 0 to 1, referring from no chance to will happen.

Answer:

the greatest common factor of this is 3

Answer:

If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution

Step-by-step explanation:

For this problem we are assumeing that the random variable X is :

[tex] X \sim Bin(n,p)[/tex]

If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution and if we don't satisfy this two conditions:

[tex] n p>10[/tex]

[tex]n(1-p) >10[/tex]

Then we can't use the normal approximation

Answer:

[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=7-1=6[/tex]  

The p value for this case would be given:

[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]

The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51

Step-by-step explanation:

Info given

50, 53, 55, 43, 50, 47, 58.

We can calculate the sample mean and deviation with this formula:

[tex]\bar X=\frac{\sum_{i=1}^n X_i}{n}[/tex]

[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2)}{n-1}}[/tex]

represent the mean height for the sample  

[tex]s=5.014[/tex] represent the sample standard deviation for the sample  

[tex]n=7[/tex] sample size  

represent the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Hypothesis to test

We want to test if the true mean is equal to 51, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 51[/tex]  

Alternative hypothesis:[tex]\mu \neq 51[/tex]  

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing we got:

[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]    

The degrees of freedom are given by:

[tex]df=n-1=7-1=6[/tex]  

The p value for this case would be given:

[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]

The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51

Assuming the coin is not weighted and is a fair and standard coin - the chance of flipping head is 1/2. You can either flip head or tails, there are no other possible outcomes.

Answer:

Answer:

A. f(x) = x^2 + 4x + 3

D. f(x) = -2x^2 - 8x + 1

Step-by-step explanation:

The axis of symmetry is found by h = -b/2a  where ax^2 +bx +c

A. f(x) = x^2 + 4x + 3

  h = -4/2*1 = -2    x=-2

B. f(x) = x^2 - 4x - 5

h = - -4/2*1 = 4/2 =2  x=2  not -2

C. f(x) = x^2 + 6x + 2

h =  -6/2*1 = -3/2 =  x=-3/2  not -2

D. f(x) = -2x^2 - 8x + 1

h = - -8/2*-2 = 8/-4 =-2  x=-2  

E. f(x) = -2x^2 + 8x - 2

h = - 8/2*-2 = -8/-4 =2  x=2  not -2

Answer:

Hey there! The answer to this question is

A. f(x) = x^2 + 4x + 3

D. f(x) = -2x^2 - 8x + 1

the answer is the bottom left option

Answer:

Step-by-step explanation:

k = 3 ; 2k + 2 = 2*3 + 2 = 6 + 2 = 8

k = 4;  2k + 2 = 2*4 + 2 = 8 +2 = 10

k =5; 2k + 2 = 2*5 +2 = 10+2 = 12

k=6;  2k +2 = 2*6 + 2 = 12+2 = 14

k = 7 ; 2k + 2 = 2*7 +2 = 14 +2 = 16

k = 8 ; 2k + 2 = 2*8 + 2 = 16 +2 = 18

∑ (2k + 2) = 8 + 10 + 12 + 14 + 16 + 18 = 78

Answer:

The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.96\frac{0.000586}{\sqrt{59}} = 0.0002[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 0.2905 - 0.0002 = 0.2903 mm

The upper end of the interval is the sample mean added to M. So it is 0.2905 + 0.0002 = 0.2907 mm

The 95 percent confidence interval for the true mean metal thickness is between 0.2903 mm and 0.2907 mm

Answer:

[tex] \frac{1}{6} [/tex]

Step-by-step explanation:

the ways of choosing 2 cards out of 4, is calculator by

[tex] \binom{4}{2} = 6[/tex]

so, 6 ways to select 2 cards.

but in only one way we can have 2 even cards. thus, the answer is

[tex] \frac{1}{6} [/tex]

Answer:

-1(3 - y)

Step-by-step explanation:

If you factor out a negative 1, you will get the opposite signs you already have, so -1(3 - y). To check, we can simply distribute again:

-3 + y

So our answer is 2nd Choice.

Answer:

C. 35

55 degrees + 35 degrees= 90 degrees

Answer:

n^2+3

Step-by-step explanation:

As we can see in the diagram

1st pattern consists from 1 square 1x1 +3 squares 1x1 each

2nd pattern consists from 1 square 2x2 +3 squares 1x1 each

3-rd pattern consists from 1 square 3x3 +3 squares 1x1 each

4-th pattern consists from 1 square 4x4 + 3 squares 1x1  each

We can to continue :

5-th pattern consists from 1 square 5x5+3 squares 1x1 each

So the nth    pattern consists from 1 square nxn+3 squares 1x1 each

Or total amount of 1x1 squares in nth pattern N= n^2+3

The expression for the numbers of squares in the nth pattern of the sequence is  [tex]n^{2} +3[/tex].

"The nth term of a sequence is a formula that enables us to find any term in the sequence. We can make a sequence using the nth term by substituting different values for the term number(n) into it."

From the given diagram

We can see that every term is made up with a square which side is n and three small square side is 1.

So,

1st term is 1 × 1 + 3 = 4

2nd term is 2 × 2 + 3 = 4

3rd term is  3 × 3 + 3 = 12

4th term is 4 × 4 + 3 = 19

So, nth term is [tex]n^{2} +3[/tex]

Hence, The expression for the numbers of squares in the nth pattern of the sequence is  [tex]n^{2} +3[/tex].

Learn more about nth term of a sequence here

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Answer:

AB=4

Step-by-step explanation:

The transitive property states if A=B and B+C than A+C  Next substitute

AB=x and x=4 so AB=4

Hope this helps, if it did, please give me brainliest, it helps me a lot. :)

Have a good day!

Answer:

Here you go!! :)

Step-by-step explanation:

Given that the sides of the quadrilateral are 3.3

The measure of one angle is 116°

We need to determine the value of x.

Value of x:

Since, the given quadrilateral is a rhombus because it has all four sides equal.

We know the property that the opposite sides of the rhombus are equal.

The measure of the opposite angle is 116°

x = measure of opposite angle

x = 116°

Then, the value of x is 116°

Therefore, the value of x is 116°

Answer:

In the diagram, the measurement of x is 87°

Step-by-step explanation:

In this diagram, this shape is a quadrilateral. This quadrilateral in this picture is known as rhombus. In a rhombus, the consecutive angles are supplementary meaning they have a sum of 180°. Consecutive means the angles are beside each other. So, we will subtract 93 from 180 to find the value of x.

180 - 93 = 87

The measurement of x is 87°

Answer:

a) 82

b) 97

Step-by-step explanation:

a) 354 - (95+95)

354 - 190

164

164 ÷ 2 = 82

(82+82+95+95=254)

b) 8439 cm^2 = 87x

8439 cm^2 ÷ 87 = 87x ÷ 87

97 = x

Answer:

1/3 feet.

Step-by-step explanation:

The length = area / width

= 7/9 / 2 1/3

= 7/9 / 7/3

= 7/9 * 3/7

= 3/9

= 1/3 feet,

Answer:

The answer is option A

4 x ( 9 + 6)

Hope this helps you

Answer:

The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].

Step-by-step explanation:

The equation of the curvature is:

[tex]\kappa = \frac{|\dot {x}\cdot \ddot {y}-\dot{y}\cdot \ddot{x}|}{[\dot{x}^{2}+\dot{y}^{2}]^{\frac{3}{2} }}[/tex]

The parametric componentes of the curve are:

[tex]x = 6\cdot e^{t} \cdot \cos t[/tex] and [tex]y = 6\cdot e^{t}\cdot \sin t[/tex]

The first and second derivative associated to each component are determined by differentiation rules:

First derivative

[tex]\dot{x} = 6\cdot e^{t}\cdot \cos t - 6\cdot e^{t}\cdot \sin t[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot \sin t + 6\cdot e^{t} \cdot \cos t[/tex]

[tex]\dot x = 6\cdot e^{t} \cdot (\cos t - \sin t)[/tex] and [tex]\dot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t)[/tex]

Second derivative

[tex]\ddot{x} = 6\cdot e^{t}\cdot (\cos t-\sin t)+6\cdot e^{t} \cdot (-\sin t -\cos t)[/tex]

[tex]\ddot x = -12\cdot e^{t}\cdot \sin t[/tex]

[tex]\ddot {y} = 6\cdot e^{t}\cdot (\sin t + \cos t) + 6\cdot e^{t}\cdot (\cos t - \sin t)[/tex]

[tex]\ddot{y} = 12\cdot e^{t}\cdot \cos t[/tex]

Now, each term is replaced in the the curvature equation:

[tex]\kappa = \frac{|6\cdot e^{t}\cdot (\cos t - \sin t)\cdot 12\cdot e^{t}\cdot \cos t-6\cdot e^{t}\cdot (\sin t + \cos t)\cdot (-12\cdot e^{t}\cdot \sin t)|}{\left\{\left[6\cdot e^{t}\cdot (\cos t - \sin t)\right]^{2}+\right[6\cdot e^{t}\cdot (\sin t + \cos t)\left]^{2}\right\}^{\frac{3}{2}}} }[/tex]

And the resulting expression is simplified by algebraic and trigonometric means:

[tex]\kappa = \frac{72\cdot e^{2\cdot t}\cdot \cos^{2}t-72\cdot e^{2\cdot t}\cdot \sin t\cdot \cos t + 72\cdot e^{2\cdot t}\cdot \sin^{2}t+72\cdot e^{2\cdot t}\cdot \sin t \cdot \cos t}{[36\cdot e^{2\cdot t}\cdot (\cos^{2}t -2\cdot \cos t \cdot \sin t +\sin^{2}t)+36\cdot e^{2\cdot t}\cdot (\sin^{2}t+2\cdot \cos t \cdot \sin t +\cos^{2} t)]^{\frac{3}{2} }}[/tex]

[tex]\kappa = \frac{72\cdot e^{2\cdot t}}{[72\cdot e^{2\cdot t}]^{\frac{3}{2} } }[/tex]

[tex]\kappa = [72\cdot e^{2\cdot t}]^{-\frac{1}{2} }[/tex]

[tex]\kappa = 72^{-\frac{1}{2} }\cdot e^{-t}[/tex]

[tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex]

The curvature is modelled by [tex]\kappa = \frac{e^{-t}}{6\sqrt{2}}[/tex].

Answer: a) additive inverse (addition)

              b) multiplicative inverse (division)

Step-by-step explanation:

Step 2: 6 is being added to both sides

Step 4: (3/4) is being divided from both sides

It is difficult to know what options are provided in the drop-down menu without seeing them. If I was to complete a proof and justify each step, then the following justifications would be used:

Step 2: Addition Property of Equality

Step 4: Division Property of Equality

Answer:

Jill bought 16 books and Sam bought 9 books

Step-by-step explanation:

Let the number of books that Jill bought be j.

Let the number of books that Sam bought be s.

Jill bought 7 more books than Sam:

j = 7 + s

They bought 25 books altogether:

j + s = 25

Put j = 7 + s into the second equation:

7 + s + s = 25

7 + 2s = 25

2s = 25 - 7 = 18

s = 18/2 = 9 books

Therefore:

j = 7 + s = 7 + 9

s = 16 books

Jill bought 16 books and Sam bought 9 books.

Answer:

Solution,

Complement of 70°

=90°-70°

=20°

hope this helps...

Good luck on your assignment..

Answer:

20°

Step-by-step explanation:

Complement of 70° is 90°-70°= 20°  

To determine the complement, subtract the given angle from 90.

Hey there! I'm happy to help!

We see that if the river isn't moving at all the boat can move at 18 mph (most likely because it has an engine propelling it.)

We want to set up a proportion where our 21 miles downstream time is equal to our 15 miles upstream time so we can find the speed. A proportion is basically showing that two ratios are equal. Since our downstream distance and upstream distance can be done in the same amount of time, we will write it as a proportion.

We want to find the speed of the river. We will use r to represent the speed of the river. When going downstream, the boat will go faster, so it will have a higher mph. So, our speed going down is 18+r. When you are going upstream, it's the opposite, so it will be 18-r.

[tex]\frac{distance}{speed} =\frac{21}{18+r} = \frac{15}{18-r}[/tex]

So, how do we figure out what r is now? Well, one nice thing to know about proportions is that the product of the items diagonal from each other equals the product of the other items. Basically, that means that 15(18+r) is equal to 21(18-r). This is a very nice trick to solve proportions quickly. We see that we have made an equation and now we can solve it!

15(18+r)=21(18-r)

We use the distributive property to undo the parentheses.

270+15r=378-21r

We subtract 270 from both sides.

15r=108-21

We add 21 to both sides.

36r=108

We divide both sides by 36.

r=3

Therefore, the speed of the river is 3 mph.

You also could have noticed that 18mph to 21 mph is +3, and 18mph to 15 mph -3 in -3 mph, so the speed of the river is 3 mph. That would have been a quicker way to solve it XD!

Have a wonderful day!

Answer:

√75 = 5√3 and √12 = 2√3 so √75 + √12 = 5√3 + 2√3 = 7√3.

Answer:

[tex] 7\sqrt{3} [/tex]

Step-by-step explanation:

[tex] \sqrt{12} \: can \: be \: simplified \: as \: 2 \sqrt{3} \: and \: \sqrt{75} \: canbe \: simplified \: as \: 5 \sqrt{3} \\ after \: simplifying \: we \: can \: add \: them \: up \\ 2 \sqrt{3} + 5 \sqrt{3} = 7 \sqrt{3} [/tex]

Answer:

The probability that 25% or more in the sample speak Spanish is 76%.

Step-by-step explanation:

Sample of 75 Americans

If 25% or more in the sample speak Spanish, it can be deduced that 24% do not speak Spanish.

The proportion of those who do not speak Spanish is 18 (24% of 75)

Therefore, the proportion of those who speak Spanish is 57 (75 - 19)

This implies that 57/75 x 100 = 76% of the sample speak Spanish.

This 76% of the sample who speak Spanish is equal to the 25% or more who do speak Spanish in the sample.

Probability is the chance that an event may occur from many other events that could have occurred.  It is an educated guess or estimate of something or one event happening when all the events in the set are given an equal chance.

Answer:

Step-by-step explanation:

a) If we assume the annual withdrawals are at the beginning of the year, we can use the formula for an annuity due to compute the necessary savings.

The principal P that must be invested at rate r for n annual withdrawals of amount A is ...

  P = A(1+r)(1 -(1 +r)^-n)/r

  P = $60,000(1.08)(1 -1.08^-20)/0.08 = $636,215.95

__

b) 20 withdrawals of $60,000 each total ...

  20×$60,000 = $1,200,000

__

c) The excess over the amount deposited is interest:

  $1,200,000 -636,215.95 = $563,784.05

The equation of the tangent line to the curve at P(7, -2) is y = 2x -16.

For each given value of x, we substitute the coordinates of P and Q into the slope formula to find the slope mPQ.

(i) For x = 6.9:

mPQ = (2/(6 - 6.9) - (-2)) / (6.9 - 7)

= 2.22

(ii) For x = 6.99:

mPQ = (2/(6 - 6.99) - (-2)) / (6.99 - 7)

= 2.020

(iii) For x = 6.999:

mPQ = (2/(6 - 6.999) - (-2)) / (6.999 - 7)

= 2.002002

(iv) For x = 6.9999:

mPQ = (2/(6 - 6.9999) - (-2)) / (6.9999 - 7)

= 2.000200

(v) For x = 7.1:

mPQ = (2/(6 - 7.1) - (-2)) / (7.1 - 7)

= 1.818182

(vi) For x = 7.01:

mPQ = (2/(6 - 7.01) - (-2)) / (7.01 - 7)

= 1.980198

(vii) For x = 7.001:

mPQ = (2/(6 - 7.001) - (-2)) / (7.001 - 7)

= 1.998002

(viii) For x = 7.0001:

mPQ = (2/(6 - 7.0001) - (-2)) / (7.0001 - 7)

= 1.999800

By observing the pattern in the calculated slopes, we can see that as x approaches 7, the slope of the secant line PQ approaches 2.

Using the point-slope form, we have:

y - y₁ = m(x - x₁)

Substituting the values of P(7, -2), we have:

y - (-2) = 2(x - 7)

y = 2x -16

Therefore, the equation of the tangent line to the curve at P(7, -2) is y = 2x -16.

Learn more about the equation of the tangent line here:

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Answer:

n = 5

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp/ adj

tan 30 = n/ 5 sqrt(3)

5 sqrt(3) tan 30 = n

5 sqrt(3) * 1/ sqrt(3) = n

5 = n