13. g(x)=(x-3) Page 186

Answer:

$1.35

Step-by-step explanation:

15% of $9 is $1.35

(9/100)*15 = 1.53

so and $1.35

The value of x is 9.

The value of y is 41

The value of angle EBF = 56°

Given,

The angles;

∠ABD = (3x + 7)°

∠DBC = (5x + 11)°

∠FBC = (3y + 1)°

We have to find the value of x, y and ∠EBF.

Here,

∠ABC = ∠ABD + ∠ DBC

∠ABC = 90° (Right angle)

Then,

90° =  (3x + 7)° + (5x + 11)°

90 = 3x + 7 + 5x + 11

90 = 8x + 18

90 - 18 = 8x

x = 72/8

x = 9

Then,

∠ABD = (3x + 7)° = 3 × 9 + 7 = 27 + 7 = 34°

∠DBC = (5x + 11)° = 5 × 9 + 11 = 45 + 11 = 56°

Now,

∠FBC + ∠DBC = 180°(Linear pair angles)

3y + 1 + 56 = 180

3y + 57 = 180

3y = 180 - 57

y = 123/3

y = 41

Then,

∠FBC = (3y + 1)° = 3 × 41 + 1 = 123 + 1 = 124°

Next,

We have to find ∠EBF

∠EBF ≅ ∠DBC (Vertical angles)

Then,

∠EBF = 56°

We can check;

∠EBF + ∠FBC = 180°(Linear pair)

56 + 124 = 180°

Therefore,

The value of x is 9.

The value of y is 41

∠EBF = 56°

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The scores of geography, economics and science are 38, 76, 80 respectively.

Let Yakubu scored x marks in geography.

Given that the score of him in economics is twice of the score of him in geography.

So, his score in economics = 2x

Again it is given that, the score in science is 4 more than the score in economics.

So the score in science = 2x+4

According to question the combined total score is 194. So the suitable equation is,

x+2x+2x+4 = 194

Solving the equation we get,

5x+4 = 194

5x = 194-4

5x = 190

x = 190/5

x = 38

So the score in geography = 38

the score in economics = 2x = 2*38 = 76

the score in science = 2x+4 = 2*38+4 = 76+4 = 80

Hence the scores of geography, economics and science are 38, 76, 80 respectively.

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AC is not perpendicular to XZ, because the slope of AC is -1 and the slope of XZ is 2/3. Therefore, the correct answer options are:

B. Is not

A. -1

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

For the slope of AC, we have the following:

Point at A = (-1, 3)

Point at C = (4, -2)

Slope, m of AC = (-2 - 3)/(4 - (-1))

Slope, m of AC = (-2 - 3)/(4 + 1)

Slope, m of AC = -5/5.

Slope, m of AC = -1.

For the slope of XZ, we have the following:

Point at X = (12, 2)

Point at Z = (6, -2)

Slope, m of XZ = (-2 - 2)/(6 - 12)

Slope, m of XZ = -4/-6.

Slope, m of XZ = 2/3.

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

-1 × 2/3 = -1

-2/3 = -1 (False).

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a) The perimeter of Martin's cat enclosure is 220 inch.

b) Martin need to buy 22 bundles each 10 ft long.

The whole distance that a rectangle's boundaries, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the sum of its four sides.

Given,

Wide = 48 inches

Length = 62 inches

a) Perimeter of enclosure:

2 × (length + width)

2× (48 + 62)

2 × 110

220

The perimeter of Martin's cat enclosure is 220 inch.

b)  Wire mesh is sold in rolls that are each 10 ft long.

Dividing it by perimeter:

220 ÷ 10

22

Martin need to buy 22 bundles each 10 ft long.

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A sequence of transformations that maps △DEF to △D′E′F′ is a  rotation of  180° about the origin followed by a translation by 1 unit to the left

We have given the graph of  triangle DEF with coordinates as;

D( -2 ,-1 )

E(-2 ,-4)

F( -1 , -1 )

Now, the coordinates of the transformed triangle D'E'F' are;

D' (1  ,1)

E' ( 1 ,4)

F' (0 ,1)

Now, the transformation rule for a rotation by 180° about the origin is (x, y) → (−x, −y) .

This means that the first transformation is a rotation of  180° about the origin to get;

D"( 2 ,1 )

E"(2 ,4)

F"( 1 , 1 )

Transformation rule ( x ,y) → (x- 1 , y) will now translate by 1 unit to the left.

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Using the properties of ratio we calculate that 680 more males than females watch the hockey match.

The given ration of males to females is 3:1.

let us consider the common ratio as a.

males = 3a

Females = a

Total number of people in the hockey match = 3a+a = 4a

Now, 4a = 1360

or, a = 340

Number of males in the match = 3a = 3 × 340 = 1020

Number of females = a = 340

Males are more by = 1020-340 = 680

An ordered pair of integers, a fraction with the value represented by this fraction as the denominator and the first number as the numerator are all examples of ratios.

Rational numbers, are also the integers and occasionally natural numbers as well, are the perfect ratios of counts that is stated in terms of (non-zero) natural numbers. When two or more numbers are compared using the same unit of measurement, which frequently occurs, their ratio is a dimensionless number.

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Answer:

56+45=101

101-90=11 °

Step-by-step explanation:

here is your answer 11°

The minimum unit cost is 8099.

Given:

A supply company manufactures copy machines. the unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made, then the unit cost is given by the function.

C(x)=0.8x^2-208x+21,619

derivative of C(x):

C'(x) = 0.8*2 x - 208+0

0 = 1.6 x - 208

1.6x = 208

divide by 1.6 on both sides

x = 208/1.6

= 208/16/10

= 208*10/16

= 2080/16

= 1040/8

= 520/4

= 260/2

x = 130

C(130) = 0.8*130^2-208*130+21619

= 16900*0.8 - 27040 + 21619

= 13520 - 5421

= 8099

Therefore the minimum unit cost is 8099.

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150cm² is the area of the given parallelogram.

So we understand that Rectangles are parallelograms.

They have the same formula for finding the perimeter and area.

Therefore, 150cm² is the area of the given parallelogram.

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The value of 2x - yz with x = 34, y = 0.2, and z = 6 we get 69.2.

Here it is given that

x = 34

y = -0.2

z = 6

We need to calculate 2x - yz

If we first calculate 2x then we get

2x = 2 X 34

= 68

Now, if we calculate -yz next then we see

yz = -0.2 X 6

= -1.2

Hence

- yz = -(-1.2)

= 1.2

Therefore, adding up these two we get

2x - yz

= 68 + 1.2

= 69.2

Hence the value of 2x - yz is 69.2

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Correct Question

Evaluate the expression 2x - yz , where x = 34 , y = -0.2, and z = 6

The annual interest rate of Niyati's invested to accumulate the accrued amount is 10%.

The formula for calculating compound interest is expressed as;

A = P( 1 + r )^t

Where A is accrued amount, P is principal , r is interest rate and t is time.

Given the data in the question;

To determine the annual interest rate, plug the given values into the equation and solve for r.

A = P( 1 + r )^t

r = (A/P)^1/t - 1

r = (( $1,210 / $1,000 )^1/2 ) - 1

r = (( 1.21 )^1/2 ) - 1

r  = 1.1 - 1

r = 0.1

Now, convert rate as percentage.

r = 0.1 × 100%

r = 10%

Therefore, the annual interest rate is 10%.

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Answer:

To create groups that are as similar as possible so the main difference between the groups is the treatment

Step-by-step explanation: got it right on khan

The product of two integers is 72. One number is two less than five times the other. Which of the following equations could be used to find one of the numbers?

A. 2x2 − 5x = 72

B. 5x2 − 2x = 72

C. 2x2 − 5 = 72

D. 5x2 − 2 = 72

ab = 72

a = 5b-2

b(5b-2)= 72

5b^2 - 2b = 72

It is B :)

Step-by-step explanation:

5x2-2+72

Answer:

53,312

Step-by-step explanation:

hope this helps :)

Answer:

Step-by-step explanation:

I believe that the price would be $ 57,120

The  slope of the line passes through the point (40,89) and (28,7) is   [tex]\frac{41}{6}[/tex].

What is slope?

It is possible to determine a line's direction and steepness by looking at its slope. Without using a compass, determining the slope of lines in a coordinate plane can assist forecast whether the lines are parallel, perpendicular, or none at all. The slope of any line can be computed using any two distinct locations on the line. Calculated using the slope of a line formula, the ratio of "vertical change" to "horizontal change" between two different locations on a line is determined.

Here the given points are

[tex](x_1,y_1)=(40,89)\\(x_2,y_2)=(28,7)[/tex]

Now using slope formula ,

=> Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m = [tex]\frac{7-89}{28-40}[/tex]

=> slope m=[tex]\frac{82}{12}[/tex]

=> slope m = [tex]\frac{41}{6}[/tex]

Hence slope of the line passes through the point (40,89) and (28,7) is   [tex]\frac{41}{6}[/tex].

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The average rate of change of g(x)=x^2 on the interval 3≤x≤9 is 12

In this question, we have been given a function g(x)=x^2

We need to find the average rate of change of function on the interval 3 ≤ x ≤ 9

For x = 3,

g(3) = 3^2

g(3) = 9

and for x = 9,

g(9) = 9^2

g(9) = 81

So, the average rate of change would be,

g(9) - g(3) / [9 - 3]

= (81 - 9) / 6

= 72/6

= 12

Therefore, the average rate of change of g(x)=x^2 on the interval 3≤x≤9 is 12

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The marked sides of a trapezoid are 8 7/8 inches long.

The Trapezoidal Rule divides the whole area into smaller trapezoids rather than utilizing rectangles to calculate the area under the curves. This integration determines the area by approximating the region beneath a function's graph as a trapezoid. The lengths for both bases and the overall perimeter are given in this issue, thus the missing sides may be determined using the following formula: Base one plus Base two (leg) equals the perimeter, where "leg" is the length of one of the two corresponding nonparallel sides.

Given,

Assuming the highlighted trapezoid's non-parallel sides.

Let a be the top of the trapezoid and b be its bottom.

a = 9 1/2

b = 22 3/4

And the trapezoid's non-parallel sides are c and d.

Using the formula for the trapezoid's perimeter,

P = a + b + c + d

50 = 19/2 + 91/4 + 2c .......(c = d)

50 = 129/4 + 2c

2c = 50 - 129/4

2c = 71/4

c = 71/8

c = 8 7/8

Consequently, the marked sides of a trapezoid are 8 7/8 inches long.

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An exponential function that best represents the value of the computer in months is V(t) = 1500(0.9763)^m.

In Mathematics, an exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be modeled by using this equation:

f(x) = ab^t

Where:

From the information provided, the value, V, of a computer is modeled by this function:

V(t) = 1500(0.75)^t

Where:

t represents the number of years since the computer was purchased.

Note: one (1) year is equal to 12 months (m).

Now, we can remodel the value of this computer in months:

V(t) = 1500(0.75)^m/t

V(t) = 1500(0.75)^m/12

V(t) = 1500(0.75^{1/12})^m

V(t) = 1500(0.9763)^m

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Answer:

y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{1}{2}[/tex]

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 the slope m of the given line using the slope formula

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

with (x₁, y₁ ) = A (- 2, 0 ) and (x₂, y₂ ) = B (4, 3 )

m = [tex]\frac{3-0}{4-(-2)}[/tex] = [tex]\frac{3}{4+2}[/tex] = [tex]\frac{3}{6}[/tex] = [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (- 5, - 2 ) into the partial equation

- 2 = - [tex]\frac{5}{2}[/tex] + c ⇒ c = - 2 + [tex]\frac{5}{2}[/tex] = [tex]\frac{1}{2}[/tex]

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

The value of n is 1, compound interest of the end of year.

What is compound interest?

The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is calculated by multiplying the starting principal amount by one and the annual interest rate raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.

When the amount compounds quarterly, it means that the amount compounds 4 times in a year. i.e., n = 4. We use this fact to derive the quarterly compound interest formula. Thus, the quarterly compound interest formula is:

A = P (1 + r/4)4t

where S= Amount at the end of n years = 3445.51

P = Principal = 2400

r = Rate of interest = 0.075

n = 1 as interest is compounded annually

Try to find it's value by solving. The number of years will be provided.

Hence the value of n is 1.

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The maximum value is; +√21 and the minimum value is; -√21

Function is a type of relation, or rule, that maps one input to specific single output.

We are given that

f(x,y,z) = x² + y² + z²

g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0

Using Lagrange multipliers as follows;

df/dx = λg/dx,

df/dy = λg/dy.

df/dz = λg/dz

Thus, df/dx = 2x, df/dy = 2y, df/dz = 2z

dg/dx = 4x³,  dg/dy = 4y³, dg/dz = 4z³

So, df/dx = λg/dx

2x = 4λx³     (1)

df/dy = λg/dy

2y = 4λy³           (2)

df/dz = λg/dz

2z = 4λz³           (3)

From (1) 4λx³ - 2x = 0

2λx³ - x = 0

x(2λx² - 1) = 0

Now solving; x = 0 or (2λx² - 1) = 0

2λx² = 1

x = ±1/√(2λ)

since x ≠ 0

From (2) 4λy³ - 2y = 0

2λy³ - y = 0

y(2λy² - 1) = 0

Now solving, y = 0 or (2λy² - 1) = 0

2λy² = 1

y = ±1/√(2λ) since y ≠ 0

From (3) 4λz³ - 2z = 0

2λz³ - z = 0

z(2λz² - 1) = 0

now solving, z = 0 or (2λz² - 1) = 0

2λz² = 1

z = ±1/√(2λ) since z ≠ 0

Then we have g(x,y,z) = x⁴ + y⁴ + z⁴ - 7 = 0

(1/√(2λ))⁴ + (1/√(2λ))⁴ + (1/√(2λ))⁴ - 7 = 0

3 (1/√(2λ))⁴ = 7

(1/√(2λ))⁴ = 7/3

1/√(2λ) = ⁴√7/3

√(2λ) = ⁴√3/7

2λ = √3/7

λ = 1/2(√3/7)

Since we know that x = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

Also, y = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

and, z = 1/√(2λ) = 1/√(2 [1/2(√3/7)]) = 1/⁴√3/7 = ±⁴√7/3

Now Substituting x,y and z into f(x,y,z) we have;

f(x,y,z) = (⁴√7/3)² + (⁴√7/3)² + (⁴√7/3)² = 3(⁴√7/3)² = 3(√7/3) = √(7 × 3) = ±√21

Hence, the maximum value is +√21 and the minimum value is -√21

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12. In the figure given, we have x, y, z parallel lines. The answers are given below.

                                    Parallel lines                               Converse

a. ∠8≅∠20                  x, z                                           x and z are parallel lines

b. ∠1≅∠9                     x, y                                           x and y are parallel lines

c. m∠3+m∠10=180°     x, y                                          x and y are parallel lines

d. ∠11≅∠16                   -                                         Opposite angles are equal

e. m∠6+m∠24=180°    x, z                                     x and z are parallel lines

f. ∠14≅∠23                  y, z                                     Opposite angles are equal

g. ∠4≅∠21                   x, z                                     x and z are parallel lines

h. m∠8+m∠18=180°     x, z                                     x and z are parallel lines

i. ∠5≅∠15                     x, y                                     x and y are parallel lines

The figure shows that x, y, z are parallel lines. m and n are trasversals drawn intersecting these parallel lines. When a transversal intersects two lines, the opposite angles are equal and the consecutive angles on the same side sum upto 180.

The corresponding angles are equal when a transversal intersects parallel lines. For example, ∠2 = ∠10 = ∠18 as they are corresponding angles and ∠2 = ∠4 and ∠4 = ∠10 as they are opposite angles.

∠2 +∠3 = 180° as they are on the same side of the transversal and are consecutive angles.

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a. The number of students that this school is going to have to enroll abroad in the year 2001 is 150

b. In the 2018 academic year, it can be said that the school would also have to enroll 468 students in the school

a. The equation is as follows:

y = 123.1 * (1.069)^x

The value of x would be years that have changed.

To get the value of x we would have to find the differences that lies in the two years.

Hence

2001 - 1998 = 3

We would place the value of x in the equation

y = 123.1(1.069)³

Then

y = 150.4

This is approximately 150.

In conclusion, There would be 150 students enrolled in the school, according to estimates, in 2001.

b. For the year 2018

We would have to carry out similar calculation

x = 2018 - 1998

This would give us  20 years difference

Place x = 20 in the equation

y = 123.1(1.069)²⁰

y = 467.5

This is approximately

y ~ 468

468 would be enrolled in the school in 2018.

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Answer:

300 ≥ 5.5 + 37.95x

Step-by-step explanation:

when she plans to drive 50 miles that means she has to pay
50 * 0.11 = 5.5
$5.5 to drive the 50 miles.
Additional to the $5.5 she has to pay the daily cost of $37.93 per day.

The total cost of renting the car therefore is
5.5 + 37.95x
with x being the amount of days.
To stay within her budget this cost can't be higher than 300
Therefore
300 greater or equal to 5.5 + 37.95x

according to this inequality, x can be no higher than 7. when x = 7 the total cost is $ 271.15
Taylor can't rent the car up to 7 days while staying within her budget.

Failure to include some units, or entire portions, of the defined survey population in the actual operational sample frame represents: a noncoverage error.

One of the components of coverage error that results from a flawed sample frame that excludes a certain percentage of the population is noncoverage.

Sampling errors need to be controlled and reduced to a level at which their presence does not defeat or obliterate the usefulness of the final sample results.

The difference between the observed values of a variable and the long-run average of the observed values in repetitions of the measurement is the sampling error.

Noncoverage, another word for these frames, inadequate coverage is also known as undercoverage.

Sampling errors can be decreased by increasing the sample size.

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Trigonometric value equal to 0 is tan 900 degrees.

What are trigonometric ratios ?

As specified by the definition of a right-angled triangle's side ratio, trigonometric ratios are the values of all trigonometric functions. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

Main Body:

The value of trigonometric ratios in the question are

assuming the function as-

Sin (30°) = 1/2

cos(360°) =1

tan (900°) = 0

cot (0°) =∞

Hence the trigonometric ratio that has value = 0 is tan(900°).

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Answer:

A, C, D

Step-by-step explanation:

edge 2023

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic as small as or smaller than that provided by the sample. For an upper tail test, the p-value is the probability of obtaining a value for the test statistic as large as or larger than that provided by the test statistic.

In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct. The p-value serves as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

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