What is the area of this triangle?

Answer:

[tex]P(Blue) = 0.3[/tex]

Step-by-step explanation:

Given

Red = 5

Blue = 3

Orange = 2

Required

Probability that the first marble is Blue

First, the total number of marble has to be calculated;

[tex]Total = Red\ Marble + Blue\ Marble + Orange\ Marble[/tex]

[tex]Total = 5 + 3 + 2[/tex]

[tex]Total = 10[/tex]

The probability of Blue being the first is calculated as thus;

[tex]P(Blue) = \frac{n(Blue)}{Total}[/tex]

[tex]P(Blue) = \frac{3}{10}[/tex]

[tex]P(Blue) = 0.3[/tex]

Hence, the required probability is 0.3

Answer: -5a²b⁵c³

Step-by-step explanation: 5ab⁴c can be thought of as 5a¹b⁴c¹ and in the second part of the problem, since there is no coefficient on -a¹b¹c², we can give it a coefficient of 1.

Now simply multiply the coefficients

and add the exponents to get -5a²b⁵c³.

Answer:

Food A = 165 grams

Food B = 23 grams

Step-by-step explanation:

Daily precise diet fed to the group:

Niacin = 41.59 units

Retinol = 17,995 units

Two food types :

Food A :

Niacin = 0.22 units per gram

Retinol = 100 units per gram

Food B:

Niacin = 0.23 units per gram

Retinol = 65 units per gram

Let:

a = gram of food A fed per day

b = gram of food B fed per day

Hence in 'a' grams of food A:

0.22a of Niacin + 100a of Retinol

In 'b' grams of food B:

0.23b of Niacin + 65b of retinol

Recall :

Total Niacin = 41.59 ; total Retinol = 17995

Then,

0.22a + 0.23b = 41.59 - - - (1)

100a + 65b = 17995 - - - (2)

From (2) ; 100a + 65b = 17995

100a = 17995 - 65b

a = 179.95 - 0.65b - - - (3)

Substitute (3) into (1)

0.22(179.95 - 0.65b) + 0.23b = 41.59

39.589 - 0.143b + 0.23b = 41.59

0.087b = 2.001

b = 2.001 / 0.087

b = 23

Put b = 23 in (3)

a = 179.95 - 0.65(23)

a = 179.95 - 14.95

a = 165

Answer:

a) Median Monthly Benefit = $439

b) The mean computed above is a STATISTIC. This is because, the mean of their monthly benefits ($455.14) was calculated from a SAMPLE (which could have been known or random) of single persons in Towson Texas.

Step-by-step explanation:

In the above question, we are given:

: $426, $299, $290, $687, $480, $439, and $565.

a) Median Monthly benefits

First we arrange the monthly benefits from the lowest to the highest

$290, $299, $426, $439, $480, $565, $687

Median Monthly Benefit is the number found in the middle of the Monthly benefits.

We were given 7 monthly benefit

$290, $299, $426,) $439, ($480, $565, $687

The median monthly benefit = $439

(b) Is the mean you computed in (a) a statistic or a parameter? Why?

The Mean Monthly Benefit = Sum of terms/Number of terms

Number of terms = 7

($290 + $299 + $426 + $439 + $480 + $565 + $687)/ 7

= $3186/7

= $455.14285714286

Approximately ≈$455.14

In the question we are asked if the Mean calculated or computed above is a Statistic or a Parameter.

The mean computed above is a STATISTIC. This is because, the mean of their monthly benefits ($455.14) was calculated from a SAMPLE (which could have been known or random) of single persons in Towson Texas.

Answer:

2(x - 8)

Step-by-step explanation:

Answer:

13 cm, 84 cm, 85 cm

Step-by-step explanation:

Let the sides of triangle are be a, b, c

As per Pythagorean theorem:

Solving the quadratic equation we get:

Then:

Answer:

Option D is the correct option

Step-by-step explanation:

[tex] \sf{(5 + 3)j = 48}[/tex]

Distribute j through the parentheses

⇒[tex] \sf{5j + 3j = 48}[/tex]

Collect like terms

⇒[tex] \sf{8j = 48}[/tex]

Divide both sides of the equation by 8

⇒[tex] \sf{ \frac{8j}{8} = \frac{48}{8} }[/tex]

Calculate

⇒[tex] \sf{j = 6}[/tex]

Hope I helped!

Best regards!!

Answer:

27

Step-by-step explanation:

FE is tangent to the circle with center D at point E and DE is radius.

[tex] \therefore FE \perp DE \implies m\angle FED = 90\degree [/tex]

DE = x

DF = x + 18

FE = 36

By Pythagoras theorem:

[tex] DF^2 = DE^2 + FE^2 [/tex]

[tex] (x+18)^2 = x^2 + 36^2 [/tex]

[tex] x^2 + 36x + 324= x^2 + 1296[/tex]

[tex] 36x + 324= 1296[/tex]

[tex] 36x = 1296-324[/tex]

[tex] 36x = 972[/tex]

[tex] x = \frac{972}{36}[/tex]

[tex] x =27[/tex]

The value of x from the given figure, which is radius of a circle is 27 units.

From the given figure, FE=36 units, DE=x units and FD=x+18 units.

Tangent and radius of a circle meet at 90°. If we draw a radius that meets the circumference at the same point, the angle between the radius and the tangent will always be exactly 90°.

Using Pythagoras theorem, we have

FD²=FE²+DE²

⇒ (x+18)²=36²+x²

⇒ x²+36x+324=1296+x²

⇒ 36x=1296-324

⇒ 36x=972

⇒ x=972/36

⇒ x=27 units

Hence, the value of x from the given figure, which is radius of a circle is 27 units.

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Two Thousand Two Hundred

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Have a great day/night!

❀*May*❀

Answer:

Two and Two Tenths.

Step-by-step explanation:

The whole number if you were to just say it is two, so you have that part, but then for the decimals, the zeros don't really matter you can take them off and you have the same number ( but only if there is nothing after the zeros) so now you are left with 2.2 and the first decimal spot is the tenths so the wording for this would Two and Two Tenths.

Answer: y=3/2x-13/2

Step-by-step explanation:

concept to know: two parallel lines have the same slope

y=3/2x+b

in order to find b or the y-intercept, we plug the point in

y=3/2x+b

1=3/2(5)+b

1=15/2+b

b=-13/2

----------------------------

y=3/2x-13/2

Hope this helps!! :)

Answer:

97%

Step-by-step explanation:

Average = x1 + x2 + x3 + x4 + x5 ........ + xN

                  ------------------------------------------

                                          N

N = total numbers

=> (89 + 98 + 96 + x) / 4 = 95

=> (283 + x) /4 = 95

=> (283+ x) / 4 * 4 = 95 * 4

=> 283 + x = 380

=> 283 -283 + x = 380 - 283

=> x = 97

I divided the sum of all numbers by 4 we are adding 4 numbers.

So, she needs to get 97% in the last test in order to have an average score of 95%

Answer:

64868 feet

Step-by-step explanation:

The deepest point as a negative 35,840 feet mark

The tallest point has a positive 29,028 feet mark

The difference between them:

Answer is 64,868 feet

Answer:

[tex]3\sin\theta+2\cos\theta=\dfrac{17}{5}[/tex]

Step-by-step explanation:

Given that,

The value of [tex]\tan\theta=\dfrac{3}{4}[/tex]

We know that, [tex]\tan\theta=\dfrac{\text{perpendicular}}{\text{base}}[/tex]

[tex]H^2=B^2+P^2[/tex]

H is hypotenuse

[tex]H^2=3^2+4^2\\\\H=5[/tex]

[tex]\sin\theta=\dfrac{P}{H}\\\\=\dfrac{3}{5}[/tex]

And, [tex]\cos\theta=\dfrac{B}{H}=\dfrac{4}{5}[/tex]

So,

[tex]3\sin\theta+2\cos\theta=3\times \dfrac{3}{5}+2\times \dfrac{4}{5}\\\\=\dfrac{9}{5}+\dfrac{8}{5}\\\\=\dfrac{17}{5}[/tex]

So, the value is 17/5.

Answer:

1

Step-by-step explanation:

Hello!

To find f(3) we put 3 in for x

[tex]3^{2} -5(3)+7[/tex]

Follow PEMDAS

9 - 5(3) + 7

9 - 15 + 7

-6 + 7 = 1

The answer is 1

Hope this helps!

Answer:

f(3) = 1

Step-by-step explanation:

f(x) = x^2 – 5x + 7

f(3) = 3^2 - 5(3) + 7

f(3) = 9 - 15 + 7

f(3) = -6 + 7

f(3) = 1

Answer:

12.25

7 percent of 175 = 12.25

(example attached below)

Answer:

7y-15

Step-by-step explanation:

10y-3(y+5)

=10y-3y-15

=7y-15

Hope it helped :)

Answer: - A horizontal shift of 3 units to the left.

- A vertical dilation of factor 2.

- A vertical shift of 6 units down.

Step-by-step explanation:

Here we have 3 transformations:

I will start giving general cases for each transformation:

Horizontal shift.

When we have a function f(x), an horizontal shift to the right of N units (N positive) is written as:

g(x) = f(x - N)

So in our case, we have a shift to the LEFT of 3 units.

Vertical dilation/contraction.

A vertical dilation/contraction of factor A, is written as:

g(x) = A*f(x)

if A > 1, this is a dilation, if A < 1, this is a contraction.

In the case of our problem, we have A  = 2.

Vertical shift:

A vertical shift is written as:

g(x) = f(x) + N.

If N is positive, we have a shift of N units up, if N is negative, we have a shift of N units down.

in this case, N = -6.

Then the transformations are:

q(x) = 2*p(x -(-3)) - 6

- A horizontal shift of 3 units to the left.

- A vertical dilation of factor 2.

- A vertical shift of 6 units down.

Answer:

Actually, this is equal to 1.

Step-by-step explanation:

Hello, please consider the following.

First of all, we assume x and y different from 0.

[tex]xy=4\\\\y=\dfrac{4}{x}\\\\x=\dfrac{4}{x}\\\\\text{So}\\\\y'(x)=\dfrac{-4}{x^2}\\\\y''(x)=\dfrac{-4*(-2)}{x^3}=\dfrac{8}{x^3}\\\\x''(y)=\dfrac{8}{y^2}\\\\\text{So, we can conclude}[/tex]

[tex]\dfrac{d^2y}{dx^2}\cdot \dfrac{d^2x}{dy^2}=\dfrac{8}{x^3}\cdot\dfrac{8}{y^3}\\\\=\dfrac{64}{(xy)^3}\\\\\text{We replace xy by 4}\\\\=\dfrac{64}{4^3}\\\\=\dfrac{64}{64}\\\\=\large \boxed{\sf \bf \ 1 \ }[/tex]

Thank you

Answer:

797.42

Step-by-step explanation:

Given the Output of a linear regression data using R;

From the result table;

Intercept = 72.807562

Gradient or slope = 0.009792

General form of a linear equation:

y = mx + c

Where y = response variable ; x = explanatory variable ; c = intercept and m = gradient / slope

Hence, the regression equation becomes :

y = 0.009792x + 72.807562

Using these regression results, what is the estimated repair cost on a car that has 74,000 miles on it?

x = 74,000

y = 0.009792(74000) + 72.807562

y = 724.608 + 72.807562

y = 797.42

Answer:

The estimated repair cost on a car that has 74,000 miles on it is $797.42.

Step-by-step explanation:

The statement: Im(formula = Repair.Costs ~ Miles.Driven, data = Dataset) implies that the variable "Repair.Costs" is the dependent variable and the variable "Miles.Driven" is the independent variable.

From the provided data the regression equation formed is:

[tex]\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}[/tex]

Compute the estimated repair cost on a car that has 74,000 miles on it as follows:

[tex]\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}[/tex]

                     [tex]=72.807562+0.009792\cdot 74000\\\\=72.807562+724.608\\\\=797.415562\\\\\approx 797.42[/tex]

Thus, the estimated repair cost on a car that has 74,000 miles on it is $797.42.

Answer:

-9/4, 2.1, -26/13, -13/8

Step-by-step explanation:

The equations of the two tangents are; Larger slope;  y = (5/7)x Smaller slope;  y = (-5/7)x

Slope tells how vertical a line is.

The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.

To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.

This is because the more the height of the line to thee amount we walk or run on the horizontal axis, the more the slope is. Thats why we took difference of horizontal axis in denominator and difference of vertical axis on numerator.

The curve x = 7 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and we need to find their equations.

We can write

 cos(t) = x/7

so

 y = 5(±√(1 -(x/7)^2)*x/7

Then

 y' = (±5/7)*(√(1 -(x/7)^2) + x/(2√(1 -(x/7)^2)*(-2(x/7))

The limit as x → 0 is ±5/7

The equations of the two tangents are;

Larger slope;  y = (5/7)x

Smaller slope;  y = (-5/7)x

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x+y+z=1

x=1/(y+z)

1/(y+z)-2y+3z=2  

1-2y²-2yz+3yz+3z²=2(y+z)

(1-2y²+yz+3z²)/2=y+z

z=(1-2y²+yz+3z²)/2 -y/1

z=(1-2y²+yz+3z²-2y)/2

Answer:

Keiko would pay $30 a month at bank A.

Keiko would pay $15 a month at bank B.

Both bank A and bank B combined would be $45 a month.

Step-by-step explanation:

Answer:

he makes $12 an hour

Step-by-step explanation:

Ed makes $6 in one hour.

To find out how much Ed makes in one hour, we can divide the total amount he makes in a 7 1/2 hour day by the number of hours in a day.

First, let's convert 7 1/2 hours to a mixed fraction.

7 1/2 hours = 7 + 1/2 = 14/2 + 1/2 = 15/2 hours.

Now, we can calculate how much Ed makes per hour by dividing the total amount he makes ($90) by the number of hours (15/2):

Amount per hour = $90 ÷ (15/2) = $90 × (2/15) = $6.

Therefore, Ed makes $6 in one hour.

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Answer: a. variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE

Step-by-step explanation:

The coefficient of determination is denoted by R square is the proportion of the variance in the dependent variable that is predictable from the independent variable.

Given:  dependent variable = TEST SCORE

independent variable = HOURS SPENT STUDYING

coefficient of determination = 0.43

That means variation in the variable, HOURS SPENT STUDYING explains 43% of the variation in the variable. TEST SCORE.

Hence, the correct option is a.

Answer:

t=3 years

Step-by-step explanation:

t=log1.05E250

t= time in years

E= ending balance.

Interest=5% per year

Ending balance=$289.41

Note: write Log 1.05 as written in the question

t= log1.05 E/250

=log1.05 (289.41 / 250)

=Log 1.05 (1.15764)

=Log (1.15764) / log (1.05)

= 0.0636 / 0.0212

=3

Therefore,

t=3 years

Answer:

D. True because the null space of an m x n matrix A is a subspace of [tex]$R^n$[/tex]

Step-by-step explanation:

A null space is also  the vector space.

We know that a null set satisfies the following properties of a vector space.

Now let [tex]$x,y \in Null (A), \alpha \in IR$[/tex] ,  then

[tex]A[\alpha x+y] = \alpha A(x)+ A(y) = \alpha . 0 + 0 = 0$[/tex]

Thus, [tex]$ \alpha x+y \in Null (A)$[/tex]

Hence, option (d) is true.

Answer:

8⋅(3a+9b−5c)

Step-by-step explanation:

The equation in a simple form by using the greatest common factor is

8 ( 3a + 9b -5c ).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The greatest common factor is the largest positive number which can be divided into given numbers evenly.

The expression will be simplified as below:-

E = 24a + 72b - 40c

Take the number 8 common from the expression.

E = 8 ( 3a + 9b -5c ).

Therefore, the equation in a simple form by using the greatest common factor is 8 ( 3a + 9b -5c ).

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Answer:

The  z-scores are   [tex]Z_{\frac{\alpha }{2} } = 0643[/tex] and  [tex]Z_{\frac{\alpha }{2} } = - 0643[/tex]

Step-by-step explanation:

From the question we are told that

    The  middle of the distribution area considered is  48%

Now the rest of the area under the standard normal distribution area is  mathematically evaluated

      [tex]\alpha = 100- 48[/tex]

      [tex]\alpha = 52 \%[/tex]

      [tex]\alpha = 0.52[/tex]

Now to obtain the area occupied by this proportion at the two tails we divide by 2 i.e

    [tex]\frac{\alpha }{2} = \frac{0.52}{2} =0.26[/tex]

Now the z-score is obtained from the normal distribution table and the value is

     [tex]Z_{\frac{\alpha }{2} } \pm 0.643[/tex]

The [tex]\pm[/tex] shows that we are considering the two-talil