Let x represent the number.
Use the given conditions to write an equation.
Solve the equation and find the number.
Four less than six times a number is the same as eight times the number. Find the number.
Question 18 options:
A)
(1/2)
B)
- (1/2)
C)
-2
D)
2
Let x represent the number.
The equation can be written as 6x - 4 = 8x.
Solving for x:
Subtracting 6x from both sides:
-4 = 2x
Dividing both sides by 2:
-2 = x
The number is -2. The answer is option C) -2.
Find the volume of the solid.
Use (22/7) for π.
14 in. 20 in.
Question 19 options:
A)
12320 cu in.
B)
616 cu in.
C)
154 cu in.
D)
3080 cu in.
To find the volume of the solid, we need to multiply the length, width, and height of the solid.
The length of the solid is 14 inches, the width is 20 inches, and the height is also 20 inches.
Volume = length * width * height
Volume = 14 in * 20 in * 20 in
Using the calculator or long multiplication:
Volume = 5600 cu in
The correct option is not listed among the choices.
Find the mode or modes.
The weights (in ounces) of 14 different apples are shown below.
table ( (5.0 5.5 4.6 6.9 4.1 5.0 5.5)(5.7 6.0 6.9 5.0 4.8 6.9 4.4) )
Question 20 options:
A)
5.0
B)
5.0, 6.9
C)
5.5, 6.9
D)
None
To find the mode or modes, we need to determine the values that occur most frequently in the dataset.
Looking at the dataset, we can identify that the values 5.0 and 6.9 both occur three times, which is the greatest frequency. Therefore, the modes of the dataset are 5.0 and 6.9.
The correct option is B) 5.0, 6.9.
Suppose ABC is a right triangle with sides of length a, b, and c and right angle at C.
Find the exact value of the indicated trigonometric function.
You may need to use the Pythagorean theorem to find the unknown side length.
Rationalize the denominator if necessary.
Find cos A when a = 9 and b = 7.
Question 21 options:
A)
(square root of (130)/7)
B)
(9square root of (130)/130)
C)
(7square root of (130)/130)
D)
(square root of (130)/9)
To find cos A, we need to use the ratios of sides in the right triangle.
In the given triangle ABC, the side opposite angle A is a and the hypotenuse is c. The cosine function is defined as the adjacent side divided by the hypotenuse.
Using the Pythagorean theorem, we can find the length of the missing side: c² = a² + b²
c² = 9² + 7²
c² = 81 + 49
c² = 130
Taking the square root of both sides:
c = √130
Now we can find cos A:
cos A = a / c
cos A = 9 / √130
To rationalize the denominator, we multiply both numerator and denominator by √130:
cos A = (9√130) / (√130 * √130)
cos A = (9√130) / 130
The correct option is C) (7√130 / 130).
Solve the problem.
3x + 12
∠1 and ∠2 are complementary angles.
What are the measures of the two angles?
Question 22 options:
A)
∠1 = 19.5°, ∠2 = 70.5°
B)
∠1 = 26°, ∠2 = 90°
C)
∠1 = 22.5°, ∠2 = 79.5°
D)
∠1 = 42°, ∠2 = 138°
Complementary angles are angles that add up to 90 degrees.
Let ∠1 represent one angle and ∠2 represent the other angle.
We can set up the equation:
∠1 + ∠2 = 90
To find the measures of the angles, we need more information or an equation relating the angles to each other. The expression 3x + 12 does not provide any such equation or information.
Therefore, we cannot determine the measures of the two angles with the given information. The correct option is D) Cannot be determined.
there is no cannot be determined
Apologies for the confusion. Given the information provided, we cannot directly determine the measures of the angles ∠1 and ∠2. Additional information or an equation relating the angles is necessary to solve the problem.
Find the area.
9 cm 15 cm 23 cm
Question 23 options:
A)
240 cm2
B)
345 cm2
C)
47 cm2
D)
207 cm2
To find the area of the given shape, we need to identify the specific shape and use the appropriate formula.
From the given information, it appears to be a trapezoid because it has one pair of parallel sides.
The formula to find the area of a trapezoid is A = (1/2)(base1 + base2)(height).
Base1 = 9 cm
Base2 = 15 cm
Height = 23 cm
Plugging these values into the formula, we get:
A = (1/2)(9 + 15)(23)
A = (1/2)(24)(23)
A = 12 * 23
A = 276 cm²
The correct option is not listed among the choices.
Find the mean of the set of data.
table ( (3.5 1.6 2.4 3.7 4.1)(3.9 1.0 3.6 4.2 3.4)(3.7 2.2 1.5 4.2 3.4)(2.7 0.4 3.7 2.0 3.6) )
Round your answer to two decimal places.
Question 26 options:
A)
3.27
B)
2.94
C)
2.80
D)
3.09
To find the mean of a set of data, we need to sum up all the values and then divide by the total number of values.
Summing up the values in the table, we get:
3.5 + 1.6 + 2.4 + 3.7 + 4.1 + 3.9 + 1.0 + 3.6 + 4.2 + 3.4 + 3.7 + 2.2 + 1.5 + 4.2 + 3.4 + 2.7 + 0.4 + 3.7 + 2.0 + 3.6 = 62.9.
There are 20 total values in the table.
Dividing the sum by the total number of values, we get:
62.9 / 20 = 3.145.
Rounding this to two decimal places, we get 3.15.
The correct option is not listed among the choices.
Find the median for the given frequency distribution.
two way table ( (Value Frequency)( 0 8)( 1 12)( 2 15)( 3 20)( 4 20)( 5 14) )
Question 27 options:
A)
3
B)
2.5
C)
3.5
D)
4
To find the median of a frequency distribution, we need to determine the midpoint value.
First, we calculate the cumulative frequency by adding up the frequencies:
0 + 8 = 8
8 + 12 = 20
20 + 15 = 35
35 + 20 = 55
55 + 20 = 75
75 + 14 = 89
The total number of observations is 89.
Since the median is the middle value, we need to find the observation that corresponds to the 45th value (the halfway point).
Looking at the cumulative frequency, we see that the 45th observation falls between the values 2 and 3.
Using the relative position of the 45th observation, we can find the exact midpoint value:
Value of the midpoint = lower boundary + (frequency / total frequency) * class width.
Class width = 1 (the difference between consecutive values)
For the range from 2 to 3, the lower boundary is 2 and the frequency is 15.
Midpoint = 2 + ( (45 - 35) / 15 ) * 1
Midpoint = 2 + (10/15)
Midpoint = 2 + 0.67
Midpoint ≈ 2.67
Therefore, the median of the given frequency distribution is approximately 2.67.
The correct option is not listed among the choices.
Find the missing length in the right triangle.
If necessary, round to the nearest tenth.
6 cm 20 cm
Question 28 options:
A)
182 cm
B)
364 cm
C)
13 cm
D)
19.1 cm
To find the missing length in the right triangle, we can use the Pythagorean theorem. The 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 other two sides.
In this case, we have the lengths of the two sides: 6 cm and 20 cm. Let's represent the missing length as x.
Using the Pythagorean theorem, we can write the equation:
x² = (20 cm)² - (6 cm)²
x² = 400 cm² - 36 cm²
x² = 364 cm²
Taking the square root of both sides gives us:
x = √364
x ≈ 19.1 cm
Therefore, the missing length in the right triangle is approximately 19.1 cm.
The correct option is D) 19.1 cm.
Solve the problem.
What is the angle of elevation of the sun when a 35-ft flag pole casts a 25-ft shadow?
Round to the nearest tenth of a degree.
Question 29 options:
A)
45.6°
B)
44.4°
C)
54.5°
D)
35.5°
To find the angle of elevation of the sun, we can use the ratio of the length of the shadow to the height of the object, which is represented by the tangent function.
The tangent of an angle is defined as the opposite side divided by the adjacent side.
In this case, the height of the flagpole is the opposite side and the length of the shadow is the adjacent side.
Let x represent the angle of elevation.
Using the tangent function:
tan(x) = Opposite / Adjacent
tan(x) = 35 ft / 25 ft
Taking the inverse tangent (arctan) of both sides to find x:
x = arctan(35/25)
x ≈ arctan(1.4)
x ≈ 53.13°
Rounded to the nearest tenth of a degree, the angle of elevation of the sun is approximately 53.1°.
The correct option is not among the choices.
Solve the problem.
5x - 4
∠1 and ∠2 are supplementary angles.
What are the measures of the two angles?
Question 30 options:
A)
∠1 = 30.67°, ∠2 = 149.33°
B)
∠1 = 30°, ∠2 = 146.00°
C)
∠1 = 30.67°, ∠2 = 153.33°
D)
∠1 = 15.67°, ∠2 = 74.33°
Supplementary angles are angles that add up to 180 degrees.
Let ∠1 represent one angle and ∠2 represent the other angle.
We can set up the equation:
∠1 + ∠2 = 180
To solve the equation, we need more information or an equation relating the angles to each other. The expression 5x - 4 does not provide any such equation or information.
Therefore, we cannot determine the measures of the two angles with the given information. The correct option is D) Cannot be determined.
Find the requested measurement.
Use π = 3.14 and round your answer to the nearest hundredth.
Find the circumference.
38 cm
Question 31 options:
A)
59.66 cm
B)
1133.54 cm
C)
238.64 cm
D)
119.32 cm
The formula to find the circumference of a circle is C = 2πr, where C represents the circumference and r represents the radius.
Given that the radius is 38 cm, we can substitute this value into the formula:
C = 2π(38 cm)
Using π = 3.14 and simplifying the expression, we get:
C = 2(3.14)(38 cm) = 239.2 cm
Rounding to the nearest hundredth, the circumference is approximately 239.20 cm.
The correct option is not listed among the choices.
Find the requested measurement.
Use π = 3.14 and round your answer to the nearest hundredth.
Find the area.
14 in.
Question 32 options:
A)
153.86 in.2
B)
43.96 in.2
C)
87.92 in.2
D)
615.44 in.2
The formula to find the area of a circle is A = πr², where A represents the area and r represents the radius.
Given that the radius is 14 in, we can substitute this value into the formula:
A = 3.14(14 in)²
Simplifying the expression, we get:
A ≈ 3.14(196 in²) = 615.44 in²
Rounding to the nearest hundredth, the area is approximately 615.44 in².
The correct option is D) 615.44 in.².
Solve and check the equation.
Begin your work by rewriting the equation without fractions.
(17y/20) - 6 = (y/4) + 6
Question 34 options:
A)
{22}
B)
{21}
C)
{20}
D)
{18}
To solve the equation, we can begin by getting rid of the fractions by multiplying every term in the equation by the least common denominator (LCD) of 20 and 4, which is 20.
Here is the equation without fractions:
20 * (17y/20) - 20 * 6 = 20 * (y/4) + 20 * 6
Simplifying, we have:
17y - 120 = 5y + 120
Now we can solve for y:
17y - 5y = 120 + 120
12y = 240
Divide both sides by 12:
y = 240/12
y = 20
To check our solution, we substitute y = 20 back into the original equation:
(17(20)/20) - 6 = (20/4) + 6
Simplifying:
17 - 6 = 5 + 6
11 = 11
The equation holds true.
Therefore, the solution to the equation is y = 20.
The correct option is C) {20}.
Solve the problem.
Cindy wants to secure sequins on a piece of felt shaped like a trapezoid with a height of 8 cm and bases of 20 cm and 14 cm.
What is the cost of all the sequins if sequins cost $0.90 per cm2 of coverage?
Question 35 options:
A)
$122.40
B)
$37.80
C)
$45.00
D)
$176.40
To solve the problem, we need to find the area of the trapezoid and then calculate the cost of sequins based on the area.
The formula to find the area of a trapezoid is A = (1/2)(base1 + base2)(height).
Plugging in the given values:
base1 = 20 cm
base2 = 14 cm
height = 8 cm
A = (1/2)(20 + 14)(8)
A = (1/2)(34)(8)
A = 136 cm²
Now, we need to calculate the cost of sequins based on the area. Given that sequins cost $0.90 per cm² of coverage, we can multiply the area by $0.90:
Cost = 136 cm² * $0.90/cm²
Cost = $122.40
Therefore, the cost of all the sequins is $122.40.
The correct option is A) $122.40.
Find the missing length in the right triangle.
If necessary, round to the nearest tenth.
18 mi 7 mi
Question 36 options:
A)
12.5 mi
B)
275 mi
C)
137.5 mi
D)
16.6 mi
To find the missing length in a right triangle, we can use the Pythagorean theorem. The 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 other two sides.
In this triangle, we have the lengths of two sides: 18 mi and 7 mi. Let's represent the missing length as x.
Using the Pythagorean theorem, we can write the equation:
x²