The Columbus Zoo conducts a study to determine whether a household’s income can be used to predict the amount of money the household will give to the zoo’s annual fund drive. The response (i.e. the effect) variable in this study is
a. the Columbus Zoo.
b. a household’s income.
c. the amount of money a household gives to the zoo’s annual fund drive.
d. all households in Columbus.

The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.

The given mass of  the metal is 611 g  and it is kept in a elevated cylinder that contains 25.1 mL of water,
Now, let us increase the water level to 56.7 mL. The metal  volume can be evaluated by subtracting the initial volume  from the final volume of water released by the metal.

Hence,
Metal volume = final volume - initial volume
= 56.7 mL - 25.1 mL
= 31.6 mL

Therefore,
Density = Mass / Volume
= 611 g/31.6 mL
= 19.3 g/cm³

The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.


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Answer:b

Step-by-step explanation:

Answer:

b and c

Step-by-step explanation:

b 5(7+6s—9t)

35+30s—45

c 10×(3.5+3s—4.5t)

10×3.5 +10×3s—10×4.5t

35+30s—45t

If the diameter of circular-garden is 18 feet, then it will cost Randy an amount of $85.50 to buy edges for his garden.

The "Circumference" of circle is defined as the "total-length" of the boundary or the outer edge of the circle.

The circumference formula is : Circumference = π × Diameter,

The "diameter" of garden is = 18-feet,

So, Circumference = 3.14 × 18 = 56.52 feet,

Since, Randy needs to buy plastic-edging to cover the entire circumference of garden, he needs to buy 56.52 feet of edging.

We know that, Randy can only buy edging in whole-foot amounts,

So, rounding up to the nearest whole foot, we get 57 feet,

The cost of edging is = $1.50 per foot,

So, "total-cost" for Randy to buy edging for his garden is,

⇒ Total Cost = (Cost per foot) × (Number of feet),

⇒ $1.50 × 57,

⇒ $85.50

Therefore, it will cost Randy $85.50 to buy edging for his circular garden.

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Answer:

1300 milliliters

Step-by-step explanation:

There are 1000 milliliters in one liter. so 1.3 liters would be 1300. 1.3 x 1000 = 1300.

The ratio of the lengths of the corresponding sides of the similar right triangles indicates that the length of the segment [tex]\overline{BD}[/tex] = 8 units

Similar triangles are triangles that have the same shape, and therefore, the interior angles of each triangle are congruent to the three angles in the similar triangle, however, the sizes of the triangles may be different.

The similar triangles are; ΔABD, ΔBCD, ΔACB

∠ABD ≅ ∠BCD ≅ ∠ACB (Corresponding angles in similar triangles are congruent)

[tex]\overline{AD}[/tex]/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/[tex]\overline{DC}[/tex]

4/[tex]\overline{BD}[/tex] = [tex]\overline{BD}[/tex]/16

4 × 16 = 64 = [tex]\overline{BD}[/tex]²

[tex]\overline{BD}[/tex] = √(64) = 8

The length of the segment [tex]\overline{BD}[/tex] = 8 units

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Answer:

(i) This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.

(ii) It is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.

Step-by-step explanation:

To determine whether the three squares can exactly surround a right-angled triangle, we need to use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's assume that the three squares have side lengths a, b, and c, with areas of 7 cm², 17 cm², and 10 cm², respectively. Then, we have:

a² = 7 cm²

b² = 17 cm²

c² = 10 cm²

We need to find out whether there exist values of a, b, and c that satisfy the Pythagorean theorem. If such values exist, then the three squares can surround a right-angled triangle.

We can rearrange the equations above to solve for a, b, and c:

a = √7 cm ≈ 2.65 cm

b = √17 cm ≈ 4.12 cm

c = √10 cm ≈ 3.16 cm

Now, we can check whether the Pythagorean theorem holds:

c² = a² + b²

(√10 cm)² = (√7 cm)² + (√17 cm)²

10 cm = 7 cm + 17 cm

This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.

In general, it is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.

The activity with a central angle of 54° is Kayaking and there were about 557 principals in attendance based on the prediction

The formula to calculate the central angle for an activity is:

central angle = (number of campers for the activity / total number of campers) x 360°

Using this formula, we can calculate the central angle for each activity:

Kayaking: (15/100) x 360° = 54°

Wakeboarding: (11/100) x 360° = 39.6°

Windsurfing: (7/100) x 360° = 25.2°

Waterskiing: (13/100) x 360° = 46.8°

Paddleboarding: (54/100) x 360° = 194.4°

Therefore, the activity with a central angle of 54° is Kayaking.

To make a prediction about the number of principals in attendance at the conference, we can assume that the proportion of principals in the exhibit room is similar to the proportion of principals in the whole conference.

In the exhibit room, out of 70 people, 52 were principals.

So, the proportion of principals in the exhibit room was 52/70

We can predict the number of principals in attendance at the conference as follows:

Number of principals = proportion of principals x total number of attendees

If we plug in the values, we get:

number of principals = 52/70 x 750 = 557

So, based on this prediction, we can say that there were 557 principals in attendance at the conference.

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Answer:

Step-by-step explanation:

False. Taxes and Social Security contributions are not deducted from a expressions person's total compensation and do not go to their employer.

In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression (such as addition, subtraction, multiplication, or division) is made up of numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.

False. Taxes and Social Security contributions are not deducted from a person's total compensation and do not go to their employer. They are instead often paid to government agencies or other approved beneficiaries.

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Using probability, we can find the following:

a. In the figure.

b. The probability that the first set is green is = 0.8

c. Probability that the second set is green is = 0.06

d. The probability that both the sets are green is = 0.48

e. The probability that at least one set is green is = 0.86

The likelihood that an event will occur is described by probability. There are many circumstances in real life where we may need to foresee how something will turn out. We might be able to predict the outcome of an event or we might not. At this point, we say, "There is a chance that the event will happen or not."

Here in the question,

b.

The probability that the first set is green is:

P = 1 - 0.2

= 0.8

c.

Now the first set is given as not green.

Probability that the second set is green is:

p = 0.2 × 0.3

= 0.06

d.

Now probability that both the sets are green is:

P = 0.8 × 0.6

= 0.48

e.

When both the sets are not green, probability is:

0.2 × 0.7

= 0.14

So, probability that at least one set is green is:

P = 1- 0.14

= 0.86

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Answer: 9/10

Step-by-step explanation:

Option a. The car is 115.47 feet from the building is correct for the given right triangle.

A trigonometric formula known as the rule of sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. In other words, if a triangle has angles A, B, and C opposing its sides and sides a, b, and c, then:

If a/sin(A) = b/sin(B) = c/sin(C), then

If some of the other sides and angles of a triangle are known, this formula can be used to solve for those unknown sides or angles. However, it is restricted to triangles and calls for the measurement of at least one angle and one side's length.

The situation can be depicted as a right triangle, with building 200 feet, the angle of depression is 30 degrees.

Now,

tan(30) = opposite/adjacent = 200/distance

distance = 200/tan(30) ≈ 115.47 feet

Hence, option a. The car is 115.47 feet from the building is correct for the given right triangle.

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The equation of a line perpendicular to line AB and passing through point (0,2) is y = -4x + 2.

The given line has a slope of 1/4, so the slope of any line perpendicular to it will be -4 (the negative reciprocal).

Using the point-slope form of a line, we can write the equation of the line passing through the point (0,2) with slope -4 as

y - 2 = -4(x - 0)

Simplifying, we get

y - 2 = -4x

Adding 2 to both sides, we get

y = -4x + 2

Therefore, the equation of the line passing through the point (0,2) which is perpendicular to the line y=1/4x+5 is y = -4x + 2.

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Histogram is the ideal type of graphic to depict the data from the school's random sample of 100 students.

A histogram is a representation of statistical data that makes use of rectangles to illustrate the frequency of dataset in a series of equal-sized numerical intervals.

Given that-

Thus, Histogram is the ideal type of graphic to depict the data from the school's random sample of 100 students.

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If 15% of "x" is 20% of "y", then "y" is 75 percent of "x", the correct option is (c).

The "Percentage" is defined as a way to express the proportions or rates in terms of a "relative-scale" out of 100,

We know that, 15% of "x" equals 20% of "y".

Mathematically, this can be expressed as,

0.15x = 0.20y,           ...because 15% = 0.15 and 20% = 0.20;

To find what percentage of x is y, we need to express "y" as a percentage of "x".
On solving further,

We get,

⇒ 0.15x = 0.20y,

⇒ y = (0.15x)/0.20,

⇒ y = 0.75x

It is read as "y" is read as 75% of "x".

Therefore, "y" is 0.75 times "x", or 75% of "x", Option(c) is correct.

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Answer:

x < 1.175

Step-by-step explanation:

-0.4x + 1.27 > 0.8

-0.4x > -0.47

x < 1.175

Answer:

$200

Step-by-step explanation:

Just divide 1600 by 8

1600 ÷ 8 = 200

Answer:

sara needs to save 200 monthly

Step-by-step explanation:

i just divided 1600 by 8.

hope u have a great day!!

Answer:

  144 m²

Step-by-step explanation:

You want to know the surface area of a square base pyramid with a side length of 6 m and a slant height of 9 m.

The area of the given net is the sum of the areas of 4 congruent triangles and one square. The areas of these can be found using the relevant formulas.

  SA = square area + 4 × triangle area

  SA = 6² + 4 × 1/2(6)(9) = 36 +108

  SA = 144 . . . . square meters

__

Additional comment

The area of a square of side s is A = s².

The area of a triangle with base b and height h is A = 1/2bh.

Answer:

x=4 y=3

Step-by-step explanation:

because y=3 and x=4

The expression 7∛7 - ∛128 is: 49∛7 - 8∛2.

We can simplify this expression using the fact that ∛(a * b) = ∛a * ∛b and ∛(a^3) = a.

First, let's factor ∛128 into prime factors: ∛128 = ∛(2^7) = 2 * ∛(2^5) = 2 * ∛(32).

Next, we can simplify 7∛7 as much as possible:

7∛7 = ∛(7^3) * ∛7 = 7∛(7^2) * ∛7 = 7 * 7∛7.

Now we can substitute these simplifications into the original expression:

7∛7 - ∛128 = 7 * 7∛7 - 2 * ∛32

We can simplify ∛32 as follows:

∛32 = ∛(2^5) = 2 * ∛(2^2) = 4∛2

Now, we can substitute this back into the expression:

7 * 7∛7 - 2 * ∛32 = 7 * 7∛7 - 2 * 4∛2

= 49∛7 - 8∛2

So the simplified expression is 49∛7 - 8∛2.

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The circumference of a circle: C = 67.98 cm

Radius of the circular lawn, which is difference between outer radius of  path and inner radius of path.

outer radius:  [tex]r1 = (132 + 2T)/2 = (132 + 2(22))/2 = 88 ft[/tex]

inner radius:  [tex]r2 = 132/2 = 66 ft[/tex]

radius of circular lawn is r = r1 - r2 = 22 ft

Now using formula for the area of a circle:

A = πr^2 = π(22^2) ≈ 1520.53 ft^2

To find the circumference of a circle with area 367 cm^2, we can use the formula for the area of a circle to find the radius:

[tex]A = \pi r^2 \\r^2 = A/\pi = 367/\pi[/tex]

r ≈ 10.80 cm

Then we can find the circumference using the formula for the circumference of a circle:

C = 2πr ≈ 2π(10.80) ≈ 67.98 cm

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The surface areas of the prisms are listed below:

Case 1: 94 in²

Case 2: 72 cm²

Case 3: 40.5 m²

Case 4: 39.1 mm²

Case 5: 130 ft²

Case 6: 136 m²

In this problem we find six cases of prisms, whose surface areas have to be found. Surface area is the sum of the areas of all faces in the prism. Face have either a rectangular or a triangular form, whose area formulas are:

Rectangle

A = b · h

Triangle

A = 0.5 · b ·h

Where:

Now we proceed to determine the surface areas:

Case 1

A = 2 · (4 in) · (5 in) + 2 · (3 in) · (4 in) + 2 · (5 in) · (3 in)

A = 40 in² + 24 in² + 30 in²

A = 94 in²

Case 2

A = 2 · 0.5 · (3 cm) · (4 cm) + (5 cm) · (4 cm) + (5 cm) · (3 cm) + (5 cm)²

A = 12 cm² + 20 cm² + 15 cm² + 25 cm²

A = 72 cm²

Case 3

A = 2 · (3 m) · (7 m) + 2 · (6 m) · (7 m) + 2 · (6 m) · (3 m)

A = 10.5 m² + 21 m² + 9 m²

A = 40.5 m²

Case 4

A = 2 · 0.5 · (4 mm)² + 2 · (4 mm) · (3 mm) + (5.7 mm) · (3 mm)

A = 16 mm² + 6 mm² + 17.1 mm²

A = 39.1 mm²

Case 5

A = 2 · (10 ft) · (5 ft) + 2 · (5 ft) · (1 ft) + 2 · (10 ft) · (1 ft)

A = 100 ft² + 10 ft² + 20 ft²

A = 130 ft²

Case 6

A = 2 · 0.5 · (6 m) · (4 m) + 2 · (7 m) · (5 m) + (7 m) · (6 m)

A = 24 m² + 70 m² + 42 m²

A = 136 m²

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1. The function that models the amount in the account after x years is [tex]y(x) = 200e^{0.05t}[/tex]

2. The domain is [tex]x > = 0[/tex]. The range is [tex]y > = 200[/tex]

3. After 8 years, Brian will have $298.37 in the account.

Function defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

The formula for continuous compounding is [tex]A = Pe^{rt}[/tex] where the A is the amount, P is the principal, e is Euler's number, r is the annual interest rate and t is the time in years.

Data:

A = ?

P = 200

t = ?

r = 5% = 0.05

Plugging in the values, we get: [tex]A = 200e^{0.05t}[/tex]which is the function.

2. The domain of the function is x >= 0 which means the number of years must be non-negative.

The range of the function is y >= 200 since the amount in the account cannot be negative and it starts with an initial investment of $200.

3. To get amount in the account after 8 years, we will plug in x = 8 into the formula:

[tex]y = 200 * e^{0.05*8}\\y = 200 * 1.49182469764\\y = 298.364939528\\ y = $298.37.[/tex]

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We got x = 149.53 by using Pythagorean theorem.

angle of semicircle is always be 90°.

[tex]172^2=85^2+x^2[/tex]

[tex]29584=7225+x^2[/tex]

[tex]x^2=29584-7225[/tex]

[tex]=22359[/tex]

[tex]x=\sqrt{22359}[/tex]

[tex]\boxed{\bold{x=149.53}}[/tex]

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