A toy company puts 25 toy cars in each box.

How many toy cars are in 1,000 boxes? Use the expression 25 × 1,000 to find the answer. Then, describe the value of 25 in the result.

A. 2,500
The place value of 25 increases by 1 place to the left.
B. 2,500
The place value of 25 increases by 2 places to the left.
C. 25,000
The place value of 25 increases by 3 places to the left.
D. 25,000
The place value of 25 increases by 4 places to the left.

The equivalent expressions are 7y + 2y+y and 10y & 8m-4m+4m and 8m.

Other expressions are not equivalent

Expressions 1

The expressions are given as

4(2a+7) and 8a +7

Open the brackets

8a+28 and 8a +7

The above expressions are not equal

Expressions 2

Here, we have

7y + 2y+y and 10y

Evaluate the like terms

10y and 10y

The above expressions are equal

Expressions 3

Here, we have

8m-4m+4m and 8m

Evaluate the like terms

8m and 8m

The above expressions are equal

Expressions 4

Here, we have

9e+2(e+5) and 11 +5

Open the brackets

9e+2e+10 and 11 +5

Evaluate the like terms

11e + 10 and 11 + 5

The above expressions are not equal

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The total change in yards where the team started is 36 yards

The given parameters in the question are:

Yards per play = 4 yards

Number of plays = 9 consecutive plays

The total change in yards is the amount of yard per play multiplied by the number of plays

This is represented as

Total change = Yards per play * Number of plays

Substitute the known values in the above equation So, we have the following equation

Total change = 4 * 9

Evaluate

Total change = 36

Hence, the total change is 36 yards

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By using the concept of law of exponents,the required answers are: 5)  [tex]e^{-1} f^{-1}[/tex] and 8) [tex]b^{3}[/tex]

According to this law of exponents, exponents of numbers are added, subtracted, multiplied, and divided when numbers get multiply, divide, and number raised by another exponents.

Exponents are the power of numbers, which tells us how many time a number multiply by itself.

we have,

5)   [tex]\frac{ef^0}{e^2f}[/tex]

⇒  [tex]e^{1-2}f^{0-1}[/tex]

⇒  [tex]e^{-1} f^{-1}[/tex]

8)  [tex]a^{0}b^{6} b^{-3}[/tex]         ( [tex]a^{0}[/tex]=1 )

⇒  [tex]b^{6-3}[/tex]

⇒  [tex]b^{3}[/tex]

Hence, final answer are [tex]e^{-1} f^{-1}[/tex] and [tex]b^{3}[/tex]

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1/2 ef sinG is the expression that correctly represents the area of triangle EFG. Select option d.

Given: the triangle EFG as shown in the image

The formula for the Area of triangle is:

A = 1/2 × base(b) × height(h)  

Area of EFG = 1/2 × f × h

Using trigonometric ratio:

sin G = h/e     (opp. / hyp.)

h = e sin G

put h = g sin E into the Area of EFG:

Area of EFG = 1/2 × f × e sin G = 1/2 ef sin G

Therefore, the expression correctly represents the area of EFG is 1/2 ef sinG

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The area of one triangle is 28 cm².​

From the question, we have

area = 1/2*base*height

=  1/2*8*7

=28 cm².

Multiplication:

In mathematics, multiplying the numbers is used to find the product of two or more numbers. We carry out one of the basic mathematical operations on a regular basis. The main application that is obvious is using multiplication tables. Mathematicians use the multiplication of two integers to express the repeated addition of one number to another. These numbers can be natural numbers, fractions, integers, whole numbers, etc. M is either added to itself 'n' times or subtracted from itself when m is multiplied by n.

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50 mg be the expected mass of the sample in the year 2002, to the nearest whole number

In 1990, a sample of a radioactive isotope had an initial mass of 110 mg and decayed exponentially over time.

A measurement in 1993 revealed that the sample's mass had decayed to 90

110 mg - 90 mg = 20 mg (amount decayed in the 3 total years)

20 mg ÷ 3 years = 6.6 mg decayed per year

6.6 × 9 years (years between 1993 and 2002) = 60 mg

110 mg - 60 mg = 50 mg, rounded to 50 mg

50 mg be the expected mass of the sample in the year 2002, to the nearest whole number

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5. Based on arc and central angle relationship, m∠BCD is: B. 108°.

6. The length of arc PQ is: H. 3.14 m

7. Length of CF is: A. 6 cm.

To find the length of an arc, the formula to use is:

Arc length = ∅/360 × 2πr

5. Measure of arc AB = 72°

Measure of arc BD = 180 - measure of arc AB

Measure of arc BD = 180 - 72

Measure of arc BD = 108°

Measure of angle BCD = measure of arc BD [central angle theorem]

Measure of angle BCD = 108°

The answer is: B. 108°

6. ∅ = 60°

r = 3 m

Arc length = 60/360 × 2 × π × 3

Arc length = 3.14 m

The answer is: H. 3.14 m

7. Since the distance between the two chords, AB and CD are equal, therefore, AB = CD.

AB = CD = 12 cm

CF = 1/2(CD)

CF = 1/2(12)

CF = 6 cm.

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The distance between the light house and the farthest island is 68 miles

The distance between the light house and the farthest island can be calculated by using the distance formula

The distance formula is d=√((x2 – x1)² + (y2 – y1)²).

d=√((61 – (-7))² + (9 – 9)²)

d = √(61 +7)²

d = 68

If each unit on the graph represents 1 mile

There are 68 units in the graph, so the light house is 68 miles away the farthest island

Therefore, The distance between the light house and the farthest island is 68 miles

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We accept the null hypothesis, according to which the average amount of trash per bin is equal to 50.

acc to our question-

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Answer:

(3, 6)

Step-by-step explanation:

I hope this helps you!

Answer:

yes for helena: not sure for edwin

Step-by-step explanation:

for helena, it would be a 270 cc rotation and then scale

for edwin, again im not sure, but it could be a refection and then scale

Step-by-step explanation:

the standard form is

f(x) = y = a(x - h)² + k

(h, k) are the vertex coordinates. here (-2, -9).

a is the stretch factor.

since the parabola opens upwards, a is positive.

so, we see already :

y = a(x + 2)² - 9

to get a we need an additional point on the curve. we see e.g. (1, 0) :

0 = a(1 + 2)² - 9 = a×3² - 9 = 9a - 9

9a = 9

a = 1

so, our standard form is

f(x) = (x + 2)² - 9

A. The correlation coefficient is of 0.303.

B. There are six positive and four negative.

C. The point with the largest residual is (6,2).

By choosing the points (x,y) from the scatter plot and entering them into a calculator, the correlation coefficient can be calculated.

A) The coordinates of these points are:

(1,2), (1,3), (2,4), (3,4), (3,5), (4,3), (4,5), (5,5), (5,6), (6,2).

Now, using Pearson correlation we have

X Values:

∑ = 34

Mean = 3.4

∑(X - Mx)² = SSx = 26.4

Y Values:

∑ = 39

Mean = 3.9

∑(Y - My)² = SSy = 16.9

So, when X and Y Combined

N = 10

∑(X - Mx)(Y - My) = 6.4

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = 6.4 / √((26.4)(16.9))

r= 0.303

Hence, the correlation coefficient is 0.303

B) As, The difference between the observed value and the expected value, or residual, is determined as follows:

C) The largest residual using absolute value is at the point is (6,2).

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The description of the motion of the ant which is a geometric series is as follows;

a) After covering 63/32 meters, the ant will have made 6 turns

b) The distance the ant will eventually travel is 2 meters

Geometric series is an infinite sum of terms in which the ratio between consecutive terms is a constant.

The distances traveled by the ant is a geometric progression of the form;

The sum of the distance is given by the sum of the geometric progression as follow;

[tex]S_n = \dfrac{a\cdot \left(1 - r^n \right)}{(1 - r)}[/tex]

Where;

aₙ = The distance traveled in the nth turn

Sₙ = The sum of the distances

a = The first term = 1 meter

r = The value of the common ratio = 0.5 meter ÷ 1 meter = 0.5

a) The number of turns the ant will have made after covering a distance of 63/32 meters is therefore;

[tex]S_n =\dfrac{63}{32} = \dfrac{1\times \left(1 - 0.5^n \right)}{(1 - 0.5)}[/tex]

31.5 = 32 × (1 - 0.5ⁿ)

32 × 0.5ⁿ = 32 - 31.5 = 0.5

0.5ⁿ = 0.5 ÷ 32

n = ln(0.5 ÷ 32) ÷ ln(0.5) = 6

b) The distance the ant travels eventually is given by the formula for the sum to infinity of a geometric progression as follows;

[tex]S_{\infty} = \dfrac{a}{1-r}[/tex]

Which gives;

[tex]S_{\infty} = \dfrac{1}{1-0.5} = 2[/tex]

The distance the ant eventually travels is 2 meters

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The measure of each exterior angles of a regular hexagon is 60  degrees

The interior angle of the regular polygon is

d = 180(n - 2) / n

Where d is the measure of interior angle

n is the number of sides

The number of sides in a regular hexagon

d = 180(6 - 2) / 6

= 180×4 / 6

= 720 / 6

=120 degrees

The each interior angle of the regular hexagon is 120 degrees

The measure of exterior angle = 180 - The measure of interior angle

= 180 - 120

= 60 degrees

Hence, the measure of each exterior angles of a regular hexagon is 60  degrees

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The area of the model on the right is given by 96 sq cm

The correct answer option is option D.

A model represents a real object on a drawing paper.

Given that the model is triangular in shape, the model on the right is 2 times the model on the left.

Therefore, area of model on the left = area of model on the left × 2².

Area of model on the left = 24 × 4

Area of model on the left = 96 square cm.

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Answer: $372

Step-by-step explanation:

330 + (1.5% of 330) = 334.95

334.95 + (1.5% of 334.95) = 339.97425

339.97425 + (1.5% of 339.97425) = 345.073864

345.073864 + (1.5% of 345.073864) = 350.249972

350.249972 + (1.5% of 350.249972) = 355.503772

355.503772 + (1.5% of 355.503772) = 360.836392

360.836392 + (1.5% of 360.836392) = 366.248398

366.248398 + (1.5% of 366.248398) = 371.742124

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Given,

The probability of head ups of a firefly = 0.1 = 10%

The average flashes per minute is 6.

1 firefly 6 flashes per minute = 0.1 flash per second

Then,

1000 × 0.1 = 100 flashes per second

100 × 10 = 1000 flashes per 10 seconds

There will be 1000 flashes per 10 seconds.

Each flash = 0.1 lumen

40 lumens = 4 flash

70/100 = 0.7

0.7 x 4 = 2.8 = 3 fireflies.

There is 3 fireflies required to produce 40 lumens

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Answer:

The answer is 3.

Step-by-step explanation:

The highest coefficient is 3 (5x^3), the second one is 2 (4x), and the other two without coefficient are considered 1.

The value of x which makes the given expression 1/2(3x+4) = 1/2x true is -2

We have to simplify the given expression to find the value of x

1/2(3x + 4) = 1/2x

Cancel 1/2 from both sides

⇒ 3x + 4 = x

⇒ 2x = -4

⇒ x = -2

Hence, the value of x is -2 which makes the given expression true.

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The rule in expressed in function notation and slope-intercept form of a line is f(x) = 3x -2

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system

The equation of a line in slope-intercept form is y = mx + c.

Where m is the slope and c is the intercept

In order to obtain the equation of the line, we are going to pick any two convenient values of x and y from the table. Let's pick the first and last point. Thus:

point1: x₁ = 1, y₁  = 1

point2: x₂ = 4, y₂ = 10

Using the equation for 2 points:

y-y₁ / y₂-y₁ =  x-x₁ / x₂-x₁

y-1 / 10-1 = x-1 / 4-1

y-1 / 9 = x-1 /3

3(y-1) = 9(x-1)

y-1 = 3(x-1)

y-1 = 3x -3

y = 3x -3+1

y = 3x - 2

Thus, f(x) = 3x -2

Therefore, the rule in function notation, using the slope-intercept form of a line is f(x) = 3x -2

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The correct equation is f(x) = 4x³ + 6x² − x .  A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.

The value of the function is f(x). The slope of the line is m. b is either the function's value at x=0 or the position at which the line in the coordinate plane crosses the y-axis. x is the x-value. This form is called the slope-intercept form.

The slope of a linear function is calculated by rearranging the equation to its general form, f(x) = mx + c; where m is the slope.

in question f(-2) = - 6

so x= -2

In function f(x) = 4x³ + 6x² - x

F(-2) = 4(-2)³ + 6 (-2)² - (-2) = - 6

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Answer:

7^{2} + x^{2} = 16^{2}

49+x^2=256

x^2=207

x=14.387=14

Answer:

14 units

Step-by-step explanation:

To find the length of the other leg of a right triangle, where one leg is 7 units long and the hypotenuse is 16 units long, use Pythagoras Theorem.

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the legs.  

Let the legs of the right triangle be "a" and "b", and the hypotenuse be "c". Therefore:

[tex]\begin{aligned}a^2+b^2&=c^2\\a^2+7^2&=16^2\\a^2+49&=256\\a^2+49-49&=256-49\\a^2&=207\\\sqrt{a^2}&=\sqrt{207}\\a&=14.3874945...\\a&=14\;\sf(nearest\;whole\;number)\end{aligned}[/tex]

Therefore, the length of the other leg is 14 units (rounded to the nearest whole number).

Answer:

see explanation

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180°

∠ B + 72° + 36° = 180°

∠ B + 108° = 180° ( subtract 108° from both sides )

∠ B = 72°

Then

∠ B = ∠ C = 72°

this means the 2 base angles in Δ ABC are congruent , then the triangle is isosceles with the 2 legs being congruent , that is

AB = AC

Answer:

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

First, compare the negative numbers as they are smaller than positives since negatives are to the left from zero on the number line and positives are to the right.

Since - 15 is smaller than - 6, the least number is - 3:

Now compare the positives.

Therefore:

The complete order is:

Answer:

-3 < -6/5 < 1/6 < √7 < 45

Step-by-step explanation:

Now the values will be,

→ 1/6 = 0.17

→ -3 = -3

→ √7 = 2.65

→ -6/5 = -1.2

→ 45 = 45

Let's arrange in ascending order,

→ -3, -1.2, 0.17, 2.65, 45

→ -3, -6/5, 1/6, √7, 45

Hence, number -3 comes first.

large samples and small variance are combination of factors is most likely to produce a significant value  in standard deviation .

What is standard deviation?

t = x - μ/s/√n

t = √n( x- μ)/s

t will be significant when its value will be higher .

so, the answer is large samples and small variance .

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The expressions that are not polynomials are the second and third ones:

A polynomial is a lineal combination of terms of powers of variables, such that the exponents must be positive integers or zero.

So, for example, a polynomial of degree n is:

p(x) = aₙ*xⁿ + ... + a₂*x² + a₁*x + a₀

Where we also can have more than one variable.

Then, for example the first one:

-4p + 7

Is a polynomial of degree 1.

The options that are not polynomials are:

p(n) = 3 + 1/n

p(q) = q^(1/2) + 5

Which are the second and third options.

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Answer:

Those are the answers

Step-by-step explanation:

3 + 1/n

q^(1/2) + 5

The postulate that can be used to prove the two triangles are congruent is the HL this is the last option

HL is an acronym that means Hypotenuse Leg. The Hypotenuse leg theorem is used in proving angle congruency in right angle triangle.

The theorem says that, two angles of a right angle triangle that have equal

then two triangles are congruent

The figure in the problem is a right angle triangle that is sharing same hypotenuse hence the hypotenuse is equal. and one other leg is marked to be equal

Therefore, this theorem says that the two triangle are congruent

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