v= u + at, find v, when u = 12, a = 5 and t = 7

Answer:

A = 55

Step-by-step explanation:

take the two identical triangles and join them so that you get a rectangle wih sides 5 and 11. now multiply them togeter to get the are of the polynom

The area of triangle is 55 square centimeters.

Area is the amount of space occupied by a two-dimensional figure.

The formula for the area of triangle is

[tex]Area = \frac{1}{2} \times base\times height[/tex]

According to the given question.

We have a figure of a quadrilateral which is made up of four right angled tringles.

Now,

The area of a triangle with base 5cm and height 7 cm

= [tex]\frac{1}{2} \times 5\times 7[/tex]

[tex]=\frac{35}{2}[/tex]

[tex]= 17.5[/tex] square centimeters

And, the area of triangle with base 4cm and height 5cm

= [tex]\frac{1}{2} \times 4\times 5[/tex]

[tex]= 10[/tex] square centimeters

Since, the quadrilateral is made up of 2 right angled triangle with base 5cm and height 7cm and 2 right angled triangle with base 4cm and height 5cm.

Therefore, the area of quadrilateral or the given fiure

= 2( area of triangle with height 7cm and base 5cm + area of triangle with base 4cm and height 5cm )

= 2(17.5 + 10) square centimeter

= 2 × 27.5

= 55 square centimeters

Hence, the area of triangle is 55 square centimeters.

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The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.

An equation is an expression that shows the relationship between two or more variables and numbers.

Inequality is an expression that shows the non equal comparison of two or more numbers and variables

The solution set of the inequalities y ≤ x² – 3 and y > –x² + 2 is the darker region shown in the graph.

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The graphs of f(x) and g(x) are transformed function from the function y = x^2 and the solution of the set of inequalities is (±1.581, -0.5)

The complete question is in the attached image (the first graph)

From the graph, we have:

f(x) = x^2 - 3 and g(x) = -x^2 + 2

To derive y ≤  x^2 - 3, we simply change the equality sign in the function f(x) to less than or equal to.

To derive y > -x^2 + 2, we simply change the equality sign in the function g(x) to greater than

The inequalities of the graphs become

y ≤ x^2 - 3 and y > -x^2 + 2

From the graph of the above inequalities (see attachment 2), we can see that the curves of the inequalities intersect at (±1.581, -0.5)

Hence, the solution of the set of inequalities is (±1.581, -0.5)

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Answer:

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2. Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.

Pythagoras Theorem Equation

The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

Answer:

The Equation in terms of m, m^2+7m+10=0

What is substituting in the equation ?

substituting means changing or replacing the values in the given equation.

Calculation:

Given equation is (x^2+3)^2+7x^2+21=-10

            and m= X^2 + 3.

make the given equation in the form X^2 + 3,

             now,

                     (x^2+3)^2+7x^2+21=-10

                     (x^2+3)^2+7(x^2+3)=-10

             where,

                      X^2 + 3= m

              after putting the value or replacing the values

             we get, m^2+7m=-10

                      m^2+7m+10=0

          the above equation is in the form of "m".

The Equation in terms of m, m^2+7m+10=0

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Answer:

m^2+7m+10=0

Step-by-step explanation:

Give brainly lol

Answer:

$4.50

Step-by-step explanation:

Okay so, first add both.

50+40 is 90, then multiply 90 by the tax percent which is

90x5%=4.5

If expression then,

x=money that they have to pay.

5%(50+40)=x    (the original)

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Answer:

3/2y-5

Step-by-step explanation:

Answer:

The ladder is 98 inches tall in inches.

Step-by-step explanation:

⇒ 8 (feet)  × 12 (inches)  = 96 inches

⇒ Add the extra 2 inches

⇒ 98 inches tall.

The  number of pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 65% pure fruit juice is:  32 pints of 95% juice, and 48 pints of 45% juice.

Let x be the amount of 95% juice.

Let the  amount of 65% juice be 80-x

Hence:

.95x+.45(80-x)=.65(80)

.5x+36=52

Collect like term

5x=16

Divide both side by 5x

x=16/5

x=32

Therefore the number of pints of each of the two existing types of drink must be used to make 50 pints of a mixture that is 65% pure fruit juice is:  32 pints of 95% juice, and 48 pints of 45% juice.

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In the binomial distribution​ for probability function, [tex]_{n}C_{x}[/tex] represents the number of ways of obtaining x successes in n trials: True

The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.

The underlying assumptions of the binomial distribution are that each trial has exactly one possible outcome, that each trial has the same success chance, and that each trial is either independent of or mutually exclusive with every other trial.

As opposed to a continuous distribution, like the normal distribution, the binomial distribution is a frequent discrete distribution used in statistics.

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The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.

In this question we must prepare a third alloy by using correct quantity of two alloys with different copper concentrations. Required weights can be determined by applying concept of weighted average:

(32/100) · (50 lb) = (30/100) · x + (62/100) · (50 - x)

32 · 50 = 30 · x + 62 · (50 - x)

32 · 50 = 30 · x + 62 · 50 - 62 · x

32 · x = 30 · 50

x = 46.875

The metallurgist would need 46.875 lb of an alloy containing 30 % copper and 3.125 lb of an alloy containing 62 % copper to produce 50 lb of a third alloy.

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The equivalence of the equation is 5x + 48 = 5x + 3.

Since 48 cannot be equal to 3, hence there are no solution.

Given the equation; x-4[ x - 2( x + 6) ] = 5x + 3

We remove the parentheses

x-4[ x - 2( x + 6) ] = 5x + 3

x-4[ x - 2x - 12 ] = 5x + 3

x - 4x + 8x + 48 = 5x + 3

5x + 48 = 5x + 3

We can go further and collect like terms

5x - 5x + 48 = 3

48 ≠ 3

Since 48 cannot be equal to 3, hence there are no solution.

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Answer: Option 1

Step-by-step explanation:

[tex]|x+4|=2\\\\x+4=\pm 2\\\\x=-4\pm 2\\\\x=-6, -2[/tex]

Solve Absolute Value.

| x + 4 | = 2

We know either x + 4 = 2 or x + 4 = −2

x + 4 = 2 (Possibility 1)

x + 4 - 4 = 2 - 4 (Subtract 4 from both sides)

x = -2

x + 4 = −2 (Possibility 2)

x + 4 - 4 = - 2 - 4 (Subtract 4 from both sides)

x = -6

Answer: x = - 2 or x = -6

Therefore we conclude that the solution of the exercise | x + 4 | = 2, is the first number line, since both results are negative.

Answer:

Step-by-step explanation:

B :10/(x+1)  +5

Using the given regression line, it is found that the amount of loss in inventory will be of $159.39.

The regression line is:

Y = 86.43 - 38.47X

In which:

In this problem, we have that X = $6.39, hence:

Y = 86.43 - 38.47 x 6.39 = -$159.39.

The amount of loss in inventory will be of $159.39.

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The sample size required is mathematically given as

n=1454

Generally, the equation for Margin of error is  mathematically given as

[tex]M=Z_{\alpha/2} > \frac{\sigma}{\sqrt{n}}[/tex]

Therefore

[tex]M= 0.11 \leq \frac{ 2.33*1.8}{\sqrt{n}}\\\\\sqrt{n} \leq 38.127[/tex]

n=1453.69.

In conclusion, The sample size required is mathematically given as

n=1454

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[tex](2m+1)+(2n+1)=2m+2n+2\\\\=2(m+n+1)[/tex]

Answer: [tex]f^{-1}(x)=\frac{x-3}{3}[/tex]

Step-by-step explanation:

Let [tex]f(y)=x[/tex]

[tex]x=3y+3\\\\x-3=3y\\\\y=\frac{x-3}{3}\\\\\therefore f^{-1}(x)=\frac{x-3}{3}[/tex]

The amount that separates the lowest 20% of the means of yearly snowfall in the past 10 years from the highest 80% is 23.57 inches.

Given mean of 112 inches, standard deviation of 14 inches.

We are required to find the amount that separates the lowest 20% ofthe means of yearly snowfall in the past 10 years from the highest 80%.

a) Bottom 20% would have a z score of -0.8416.

b) Top 80% would have a z score of 0.842.

Use the z formula to find the raw score.

z=(X-m)/sd

X=the raw score

m= mean

sd=standard deviation

Putting the value of low score.

-0.8416=(X-112)/14

X=-11.7824+112

=100.2176

Putting the values of high score.

0.842=(X-112)/14

X=123.788

The amount that seprates the lowest from highest is 123.788-100.2176

=23.57 inches.

Hence the amount that separates the lowest 20% of the means of yearly snowfall in the past 10 years from the highest 80% is 23.57 inches.

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Answer:

(2, -11)

Step-by-step explanation:

(x + 3, y + 2) = (5, -9)

x + 3 = 5

y + 2 = -9

x = 2

y = -11

Answer: [tex]g(x)=\left(\frac{x}{5} \right)^2[/tex]

Step-by-step explanation:

See attached image.

The percentage of students that have scored more than you is 1.39%

a) Probility that people scored more than Nancy = P(X>1390) = 1- P(X<1390).

Now z= (1390-950)/200

z= 2.2

P(Z<2.2) = 0.9861

So 1- P(X<1390) = 1 - P(Z<2.2) = 1 - 0.9861 = 0.0139

= 1.39 %

Let P1 be the % of people who score below 1100 and P2 be the % of people who scored below 1200

Then % of students between scores of 1100 and 1200 = P2 - P1

Z (X=1100) =0.75 and Z (X=1200) = 1.25

P1 = P(X<1100)= P (Z< 0.75) =0.7734

P2 = P(X<1200)= P (Z< 1.25) =0.8944

Then % of student between score of 1100 and 1200 = P2 - P1 = 0.8944 - 0.7734 = 0.121 = 12.10%

Middle 87.4 % score means that a total of 12.6 % of the population is excluded. That is 6.3% from both sides of the normal curve. So the minimum value for the middle 87.4% will the one which is just above 6.3% of the population i.e. it will have value x such that P(X<x)= .063.

z value (for P(X<x)= .063) = (-1.53)

But Z= (x-u)/ \sigma from here calculating x, x=644

The minimum value of the middle 87.4% score is 644

The maximum value for the middle 87.4 % of the scores will be the one that has 6.3% scores above it, i.e. it will have value x such that P(X>x)= .063.

P(X<x)= 1 -P(X>x)= 1 - 0.063 = 0.937.

Z value (for P(X<x)= 1.53

But Z= (x-u)/ \sigma from here calculating x, x=1256

The maximum value of the middle 87.4% score is 1256

Z value for (X=1432)= 2.41

P(Z<2.41) =0.9920

It means that 99.2 % of scores are less than 1432

So only 0.8% of scores are higher than 1432

but , 0.8% = 165

So 100% = 20625

20625 students took SAT

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Answer:

(f + g)(x) = x² + 2x - 6

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 2x + 1 + x² - 7 ← collect like terms

= x² + 2x - 6 ← in standard form

Using the normal distribution, it is found that:

A. 0.0071 = 0.71% of packages will be rejected because the average weight is too low.

B. 0.96 = 96% of packages that will be accepted.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

For this problem, the parameters are given as follows:

[tex]\mu = 170, \sigma = 12, n = 6, s = \frac{12}{\sqrt{6}} = 4.9[/tex]

Item A:

The proportion is the p-value of Z when X = 158, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{158 - 170}{4.9}[/tex]

Z = -2.45

Z = -2.45 has a p-value of 0.0071.

0.0071 = 0.71% of packages will be rejected because the average weight is too low.

Item B:

The proportion that will be accepted is the p-value of Z when X = 179 subtracted by the p-value of Z when X = 158, hence:

X = 179:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{179 - 170}{4.9}[/tex]

Z = 1.84

Z = 1.84 has a p-value of 0.9671.

X = 158:

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{158 - 170}{4.9}[/tex]

Z = -2.45

Z = -2.45 has a p-value of 0.0071.

0.9671 - 0.0071 = 0.96 = 96% of packages that will be accepted.

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The composite function G(F(x)) = x² + 4 is formed with these following original functions:

D. F(x) = x² and G(x) = x + 4.

The composite function of f(x) and g(x) is given as follows:

[tex](f \circ g)(x) = f(g(x))[/tex]

For g of f(x), we have that:

[tex](g \circ f)(x) = g(f(x))[/tex]

For this problem, we have that:

G(F(x)) = x² + 4.

Which is possible with option D, as:

[tex]G(F(x)) = G(x^2) = x^2 + 4[/tex]

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Answer:

C. (2;9)

Step-by-step explanation:

for more details see the attachment.

The amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.

The future value refers to the compounded value (at an interest rate) of the present value, including the periodic cash investments, over a period.

The future value can be determined using either the future value formula, future value table, or an online finance calculator, as below.

N (# of periods) = 18 months

I/Y (Interest per year) = 15%

PV (Present Value) = R1,000

PMT (Periodic Payment) = R 700

Results

FV = R15,282.91 (R12,600 + R1,000 + R1,682.91)

Sum of all periodic payments = R12,600 (R700 x 18)

Total Interest = R1,682.91

Thus, the amount that should be in Nickey's savings account immediately after her last deposit on September 30, 2012, using the future value concept, is R15,282.91.

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Answer:

-3

Step-by-step explanation:

Select a point on the red line that crosses the graph at a corner like point (2,2).  Start at the middle of the graph and go 2 spaces to the right on the x axis and then 2 spaces up.  Now you will be a the point (2,2).  Do you see how the right line is hitting at the top left corner of the square?  

From  this point, count how many spaces up and how many spaces to the left to get to the next spot that the red line touches a corner.  If you go up 3 spaces and left 1, you have found the next corner.  The slope is -3/1 or -3.

The slope is negative because the x and y's are going in different directions, as the x is getting bigger, the why is getting smaller, or another way of looking at it, is that I went up to the find slope and up is positive, but then I went left 1 and left is toward the negative numbers.  A positive divided by a negative is a negative, so the slope is negative.

The number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8

It is important that a 2D shape arrow is a shape with 8 sides

Sum of angles of a polygon = (n - 2) × 180

⇒ ( 8 - 2) × 180

⇒ 6 × 180

⇒ 1080

The number of interior angles are 8 and this is so because of the number of sides in the 2D shape right arrow

Thus, the number of interior angles in a 2D shape right arrow is 8 because , the number of sides is also 8

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The surface area of the cone is 282.6 square centimeters.

For a cone of radius R and height H, the surface area is given by:

[tex]A = pi*R^2 + pi*R*\sqrt{R^2 + H^2}[/tex]

Where pi = 3.14

In this case, we have:

[tex]A = 3.14*(5cm)^2 + 3.14*5cm*\sqrt{(5cm)^2 + (12cm)^2} = 282.6 cm^2[/tex]

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