Tawny wrote an expression to represent “the quotient of 82 and a number, decreased by 26.” She then evaluated the expression when n = 2. Which statements are true about the expression and its value? Check all that apply.
The correct expression is 82 minus StartFraction 24 Over n EndFraction.
To evaluate the expression, subtract 26 from the quotient.
To evaluate the expression, subtract the quotient from 82.
The correct expression is StartFraction 82 Over n EndFraction minus 26.
The operations include division and subtraction.
To evaluate, substitute 24 for the variable in the equation.
The value of the expression is 15.

Answer:

4158cm cubed. Hope this helped!

Answer:

∠ABC =   52°

∠BCA =  48°

∠CAB = 80°

Step-by-step explanation:

Angle sum property of triangle: Sum of all the angles of a triangle is 180.

13x² + 12x² + 20x² = 180

Combine like terms,

                 45x²  = 180

                     x² = 180 ÷ 45

                     x² = 4

                     x = √4

                     x = ± 2

x = 2 ; -2

∠ABC = 13x² = 13*4 = 52°

∠BCA = 12x² = 12 *4 = 48°

∠CAB = 20x² = 20 *4 = 80°

The value of x is +2 and -2 and the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

Given that:-

∠ABC = 13x² ∠ACB = 12x² and ∠CAB = 20x²

The angles will be calculated as follows:-

13x² + 12x² + 20x² = 180

45x²  =  180

x²  =  4

x   =  ±2

The angles will be:-

∠ABC = 13x²  = 13 x ( 2² ) = 52

∠ACB = 12x²  = 12 ( 2² )    = 48

∠CAB = 20x²  = 20 ( 2² )  = 80

Therefore value of x is +2 and -2 the angles will be given as ∠ABC = 52 ∠ACB = 48 and ∠CAB = 80.

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Answer:

Mark will use 1.25 pounds of pork.

Step-by-step explanation:

Let b represent the number of pounds of pork and p represent the number of pounds of beef. Since the ratio of beef to pork is 3 to 1, we have b/p = 3/1, which then becomes b = 3p. From this:

[tex]3p + p = 7[/tex]

[tex]4p = 7[/tex]

[tex]p = 1.75[/tex]

[tex]b = 3 \times 1.75 = 5.25[/tex]

Answer: 1.44

Step-by-step explanation:

(original price) - (1/6 of the original price) = 1.20

If you let x = original price, then the equation is:

x - 1/6 x = 1.20

5/6 x = 1.20

x = 1.44

the original price is £1.44.

Credits to the person who also answered :)

I hope this helps!

Answer:

£1.44

Step-by-step explanation:

Since the original price was reduced by 1/6, that means the new price is 5/6 of the original price.

Let x = original price.

Write an equation and solve it.

5/6 x = £1.20

x = £1.20 × 6/5

x = £1.44

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. Mike's account balance after 21 years is $69,131.44.

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.,

[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]

where A is the final amount

P is the principal amount

r is the rate of interest

n is the number of times interest is charged in a year

t is the number of years

The principal amount that Mike invested is $29,000. The rate of interest is 7.24% compounded daily, for 21 years. Therefore, the account balance after 21 years is

[tex]\text{Account Balance after 21 years} = 29,000(1+\dfrac{0.0724}{365})^{(365 \times 21)}[/tex]

                                                     = $69,131.44

Hence, Mike's account balance after 21 years is $69,131.44.

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The lines of symmetry for all the figures have been determined.

A symmetry in which one half of the object is symmetrical to thew other half

A square has 4 lines of reflection symmetry , 2 along its sides and 2 along its diagonals

A regular hexagon has 6 reflection symmetry , three along the midpoints of the sides and three along the daigonals

A Trapezium can have 0  or 1 lines of symmetry depending upon the length of the non parallel sides.

An equilateral Triangle has 3 lines of reflection symmetry , an isosceles has 2 lines of symmetry and a scalene triangle has no lines of symmetry.

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Answer:

Step-by-step explanation:

got it right

The equivalent expression to 7^13/7^7 would be 7^6.

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple. Usually, we simplify it.

We have given an expression as  7^13/7^7

The equivalent expression;

[tex]\dfrac{7^{13}}{7^7} \\\\7^{13-7}\\\\7^6[/tex]

Hence, The equivalent expression to 7^13/7^7 would be 7^6.

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Answer:

Step-by-step explanation:

A pack of sugar costs £1.25 for 500g. How much for 1kg?

500g = 1/2Kg or 0.5 Kg

so 1.25£ is 0.5Kg (1/2)

1.25 * 2 = 2.50£ is your answer

Answer:

2.5

Step-by-step explanation:

Change 500g into kg

500g=500/1000kg

        =0.5kg

If                  0.5kg cost 1.25

what about 1kg

   = (1*1.25)/0.5

   = 1.25/0.5

   =2.5

Answer:

1.3 < x < 6.7

Explanation:

Given two sides of a triangle: 2.7 and 4.0

If 'x' will be the largest side:

If 'x' will be smallest side:

Hence range of possible size: 1.3 < x < 6.7

The option fourth "There is a strong negative relationship between x and y" is correct.

It is defined as the relation between two variables which is a quantitative type and gives an idea about the direction of these two variables.

[tex]\rm r = \dfrac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{{[n\sum x^2- (\sum x)^2]}}\sqrt{[n\sum y^2- (\sum y)^2]}}[/tex]

The options are:

We have data:

x 7 8 9 10 11 12 13

y 13 10 7 6 5 3 0

The value of correlation r = -0.9847

As we know the value of r between -1 to +1

If r = 1 (perfect and positive correlation)

if r = -1 (perfect and negative correlation)

We have r = -0.9847

The value is near to -1 which means there is a strong negative relationship between x and y.

Thus, the option fourth "There is a strong negative relationship between x and y" is correct.

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Answer:

3rd option

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, - 1) ← 2 points on the line

m = [tex]\frac{-1-(-2)}{4-0}[/tex] = [tex]\frac{-1+2}{4}[/tex] = [tex]\frac{1}{4}[/tex]

the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2

y = [tex]\frac{1}{4}[/tex] x - 2 ← equation of line

Answer:

4500 sec

Step-by-step explanation:

1hr 15min= 75 min

75 x 60=4500

Answer:

54x + 36

Step-by-step explanation:

Simplify:

First open the brackets by multiplying  each term by 7.

 5x - 6 + 7(7x + 6) = 5x - 6 + 7*7x + 7*6

                              = 5x - 6 + 49x + 42

                              = 5x + 49x - 6 + 42

Combine like terms. Like terms have same variable with same power. Here 5x and 49x are like terms & (-6) and 42 are like terms (Constants)

                              =  54x + 36

Answer:

54x +36

Step-by-step explanation:

5x - 6 + 7(7x+6)       multiply                

5x -6 +49x+42         add like terms

54x + 36                   that's the answer

Answer:

[tex]\huge\boxed{\sf BC = 19.4 \ cm}[/tex]

Step-by-step explanation:

θ = 71°

Adjacent = AB = 6.3 cm

Hypotenuse = BC = ?

We will use the trigonometric ratio of cos.

[tex]\displaystyle cos \theta = \frac{Adjacent}{Hypotenuse} \\\\cos \ 71 = \frac{6.3}{BC} \\\\0.33 = \frac{6.3}{BC} \\\\BC =\frac{6.3}{0.33} \\\\\boxed{BC = 19.4 \ cm}\\\\\rule[225]{225}{2}[/tex]

Answer:

l×b×h

50×10×20

10000cm^3

Step-by-step explanation:

please mark me as brainlest

Answer:

10000 cm³

Step-by-step explanation:

Volume of rectangular box:

         To find the volume of box,  multiply the length, width and height of the box and its unit is cubic units

         [tex]\sf \boxed{\bf Volume \ of rectangular \ box = l *w*h}[/tex]

                                                         = 50 * 1 0 * 20

                                                          = 10000 cm³

Answer: -1+3=2 and -1×3=-3

Step-by-step explanation:

This is the best answer I could give. I hope this helps!! :)

Answer:

This assumes that the question was meant to read:

"A triangle has side lengths of (7x−4) centimeters, (x+3) centimeters, and (3x+2) centimeters."  And not "A triangle has side lengths of (7x-4)(7x−4) centimeters, (x+3)(x+3) centimeters, and (3y+2)(3y+2) centimeters."

If the revision is correct, the perimeter is 11x + 1 cm

=============================================

If the question was correctly written, then answer is:

50x^2 - 50x + 9y^2  + 12 y  + 29

===============

Step-by-step explanation:

  (7x-4) cm

+ (x+3)  cm

+ (3x+2) cm

11x + 1 cm

If the question was correctly written as is, then:

(7x-4)(7x−4) = 49x^2 - 56x + 16

+(x+3)(x+3)    =     + x^2   + 6x   + 9

+(3y+2)(3y+2) = +9y^2  + 12 y  + 4

                         50x^2 - 50x + 9y^2  + 12 y  + 29 cm

The perimeter of triangle 8x+ 3y + 1.

The complete length of a triangle's boundary is referred to as its perimeter. A triangle is a polygon with three sides, and there are various varieties of triangles depending on how big the sides and angles are.

The basic formula used to calculate the perimeter of a triangle is:

Perimeter = sum of the three sides

Given:

sides of triangle  (7x-4) centimeters, (x+3) centimeters, and (3y+2).

Now, perimeter of triangle

= 7x-4 + x+ 3 + 3y+ 2

=8x + 3y + 5-4

=8x+ 3y + 1

Hence, the perimeter of triangle 8x+ 3y + 1.

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The value of an expression will be equal to -1.

The complete question is given below:-

If the value of w is -5 then find the value of the expression w² + 3w -11.

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

The given expression will be solved as follows:-

E = w² + 3w -11.

E = ( -5 )²  + ( 3 x -5 ) -11

E = 25 - -15 - 11

E = 25 - 26

E = -1

Therefore the value of an expression will be equal to -1.

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Answer:

-5.5°C > -17.5°C

Step-by-step explanation:

Since -5.5 is larger than -17.5

The correct inequality symbol to complete the inequality statement is ">" (greater than). [tex]-5.5^{\circ}C > -17.5^{\circ}C[/tex].

To understand why this symbol is used, let's compare the two temperatures.

The temperature in Moscow is -5.5C, while the temperature in Cold Lake is [tex]-17.5^{\circ}C[/tex].

Since -5.5 is greater (warmer) than -17.5,  use the ">" symbol to indicate that [tex]-5.5^{\circ}C[/tex] is greater than [tex]-17.5^{\circ}C[/tex].

Here's a step-by-step explanation:

In summary, when comparing the temperatures of Moscow and Cold Lake, the correct inequality statement is [tex]-5.5^{\circ}C > -17.5^{\circ}C[/tex], indicating that Moscow's temperature is higher (warmer) than Cold Lake's temperature.

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Step-by-step explanation:

you don't know the meaning of

[tex]y = {h}^{ - 1} (x)[/tex]

it means it is the inverse function to h(x).

the regular function assigns an y value to every x value.

the inverse function now turns this around and finds for a given y value the original x value.

so, the inverse function is easier understood, if we would write it

[tex]x = {h}^{ - 1} (y)[/tex]

but just for formal reasons, we don't define functions this way but do it like above (x is the input, y the output value).

just, the understanding of an inverse function is a I just described it.

that means for the points, simply x and y values trade places.

the point (1, 9) turns into (9, 1) (it means 1 was the original x value when the original function delivered 9 a result).

and the point (3, 2) turns into (2, 3).

so, move the 2 green dots to these coordinates.

Answer:

5.32⋅10−6

Step-by-step explanation:

Answer:

5320000

Step-by-step explanation:

standard notation form : 5320000

The mean is  6394530.35 and the median is = 3355572.5

The missing data is attached in the answer.

Mean is the average value of the data points , it is determined by dividing the total sum of the data points to the number of data points.

Mean and Median is the measure of the central; tendency of the data.

Mean is given by

Sum of the observations/number of observations

= (741894 + 6931071....)/20

= 6394530.35

2) To find median

The data needs to be arranged in ascending order

Then the median is the middle number of the arranged data

Here the median is = 3355572.5

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Answer:

Step-by-step explanation:

The volume of the cylinder shown below is 252πcm³

The formula for calculating the volume of a cylinder is expressed as:

V = πr²h

where:

r is the radius

h is the height

Given the following

radius = 6 units

height = 7 units

Substitute

V = πr²h

V = π(6)²(7)

V = 252πcm³

Hence the volume of the cylinder shown below is 252πcm³

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Answer:

2

[tex]3 \times 3[/tex]

In the ΔIJH, the value of the cosec (I) is [tex]1\frac{9}{56}[/tex].

Given ΔIJH the length of the hypotenuse is 65,  the length of the base is 33, and the length of the opposite side is 56.

We have to find the value of the cosec (I).

A function of an arc or angle that is most easily represented in terms of the ratios of pairs of sides of a right-angled triangle, such as the sine, cosine, tangent, cotangent, secant, or cosecant.

We know cosec (I) = hypotenuse / opposite side

Substitute the values

cosec (I) = 65/56

              = [tex]1\frac{9}{56}[/tex]

Hence the value of cosec (I) is [tex]1\frac{9}{56}[/tex].

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As the sample size grows, the distribution of the sampled means becomes normally distributed option (C) is correct.

With simple random sampling, each component of the population has an equal chance of being selected for the sample.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

Suppose a simple random sample of size n is obtained from a population whose distribution is skewed right.

As we know, the distribution of sample means will be normally distributed even if the individual samples do not, according to the Central Limit Theorem, if the mean values for increasing sample sizes are determined.

Thus, as the sample size grows, the distribution of the sampled means becomes normally distributed.

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