The variance of the given frequency distribution is 60.92, and the standard deviation is option (b) 7.80.
To calculate the variance of a frequency distribution, we need to first find the mean or average of the data. The formula for calculating the mean is as follows:
mean (μ) = Σfx / Σf
where Σfx represents the sum of the products of each value and its corresponding frequency, and Σf is the sum of all the frequencies.
Using the given data, we can calculate the mean as follows:
μ = (43 + 85 + 119 + 175 + 204 + 243 + 32*1) / (3+5+9+5+4+3+1)
μ = 13.5
Next, we need to calculate the deviation of each data point from the mean. To do this, we subtract the mean from each value and square the result. The formula for this is:
(x - μ)²
Using this formula, we get the following deviations for each data point:
(4 - 13.5)² = 81.00
(8 - 13.5)² = 30.25
(11 - 13.5)² = 6.25
(17 - 13.5)² = 12.25
(20 - 13.5)² = 42.25
(24 - 13.5)² = 110.25
(32 - 13.5)² = 333.22
Next, we need to multiply each deviation by its corresponding frequency, and then sum up the results. The formula for this is:
Σf(x - μ)²
Using the above deviations and frequencies, we can calculate the sum of squares as follows:
Σf(x - μ)² = 381.00 + 530.25 + 96.25 + 512.25 + 442.25 + 3110.25 + 1 x 333.22
Σf(x - μ)² = 1827.48
Finally, we can calculate the variance by dividing the sum of squares by the total number of observations (Σf). The formula for variance is:
σ² = Σf(x - μ)² / Σf
Using the above values, we can calculate the variance as follows:
σ² = 1827.48 / 30
σ² = 60.92
The standard deviation is the square root of the variance. Therefore:
σ = √(60.92)
σ = 7.80
Therefore, the correction option is (b).
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Complete Question:
Find the variance and standard deviation of the following frequency distribution:
x 4 8 11 17 20 24 32
f 3 5 9 5 4 3 1
If n=540 and
(p-hat) = 0.64, construct a 90% confidence interval.
Give your answers to three decimals.
__ < p < __
Answer:
0.606 < p < 0.674
Step-by-step explanation:
[tex]\displaystyle CI=\hat{p}\pm z\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\CI_{90\%}=0.64\pm1.645\sqrt{\frac{0.64(1-0.64)}{540}}\\\\CI_{90\%}\approx0.64\pm0.034\\\\CI_{90\%}=\{0.606,0.674\}[/tex]
Thus, we are 90% confident that the true population proportion is between 0.606 and 0.674
which answer choice is the correct one
Solve: 6(x + 5) = -2(x-3)
Answer:
Step-by-step explanation:
6(x+5) = 6x+30
-2(x-3)=-2x+6
6x+30=-2x+6
8x+30=6
8x=-24
x=-3
Answer: x = -3
Step-by-step explanation:
6(x + 5) = -2(x-3)
1. Distribute: 6x + 30 = -2x + 6
2. Add 2 to both sides: 8x + 30 = 6
3. Subtract 30 on both sides: 8x = -24
4. Divide by 8 on both sides: x = -3
Find the direction of the sum of
these two vectors:
30.0°
6.00 m
5.00 m
The direction of the sum of the two vectors is along the west direction
How to find the direction of the sum of the two vectorsAssuming vector A is pointing west ward and vector B is pointing eastward
The direction of vector A to the horizontal is negative solved by
= -6 cos 30
= -5.196
Adding both vectors
= vector A + vector B
= -5.196 + 5
= -0.196
Hence the direction is to the west since it is negative
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Explain how you would solve negative x = 9 algebraically what inverse operation ?should be used is there an invisible number in front of x ?if so what is it? if not how do you solve this?
The solution to the equation "negative x = 9" is "x = -9". There is no invisible number in front of "x" in this equation.
Solving the equation "negative x = 9" algebraicallyTo solve the equation "negative x = 9" algebraically, we want to isolate the variable "x" on one side of the equation.
First, we notice that "negative x" means "-x", so we can rewrite the equation as:
-x = 9
To isolate "x", we need to perform an inverse operation on both sides of the equation. Since "-x" means the opposite of "x", we need to perform the opposite operation, which is to add "x" to both sides:
-x + x = 9 + x
Simplifying the left-hand side by canceling out the "-x" and "+x", we get:
0 = 9 + x
We can further simplify this equation by subtracting 9 from both sides:
0 - 9 = 9 + x - 9
-9 = x
So the solution to the equation "negative x = 9" is "x = -9".
There is no invisible number in front of "x" in this equation, so we don't need to worry about any additional steps or calculations.
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Jan, Freda and Pieter share some money.
Freda gets 3 times as much as Jan.
Pieter gets half as much as Freda.
(a) Write down the ratio of the amounts of money that they each get.
Give your answer in its simplest form.
The ratio of the amounts of money that they each get:
1 : 3 : 3/2
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Let's represent the amount of money that Jan gets as x.
Then, the amount of money that Freda gets is 3x,
and the amount of money that Pieter gets is:
= (1/2) x 3x
= 3/2 x (x)
The ratio of the amounts of money that they each get can be written as:
⇒ x : 3x : 3/2 x (x)
⇒ 1 : 3 : 3/2
So, Jan gets 1 unit of money, Freda gets 3 units of money, and Pieter gets 3/2 units of money.
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Smaller metric unit to a larger unit:
6,000 grams
kilograms
6,000 grams is equivalent to 6 kilograms.
How to convert the unitsThe problem is solved by converting the given dimensions from grams to kilograms. The conversion is from a smaller metric unit to a larger metric unit.
A kilogram is a larger unit of measurement for mass or weight compared to a gram.
The prefix kilo in kilogram means 1000, so one kilogram is equal to 1000 grams.
Therefore, to convert from grams to kilograms, you simply divide the number of grams by 1000.
In this case, 6,000 grams divided by 1000 equals 6 kilograms.
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she reads the meter again after one month when they move in 789 units after one month 820 units
The units of water the friends used in one month is 820 units.
How many units of water did the friends use in one month? Meter reading when they moved in = 789 unitsMeter reading after one month of moving in = 820 unitsThe total units of water used as read by the meter = 789 units + 820 units
= 1609 units
Therefore, the friends used a total of 820 units of water.
Complete question:
A water meter shows how many units of water Riya and her friends use.
Riya reads the meter when they move in. It shows 789 units.
She reads the meter again after one month. It reads 820 units.
How many units of water did the friends use in one month?
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help help help help help help help help help help help help help help help help help help help help
Find the number of sides of a regular polygon in which each exterior angle has a measure of 6
Answer:
Below
Step-by-step explanation:
The exterior angles for any polygon sum to 360 °
so
6 * n = 360 ° <===== where 'n' is the number of sides
n = 60 sides
5 Heena and Sudha share Profit & Loss equally. Their capitals were Rs.1,20,000 and Rs. 80,000 respectively. There was also a balance of Rs. 60,000 in General reserve and revaluation gain amounted to
Rs. 15,000. They admit friend Teena with 1/5 share. Teena brings Rs.90,000 as capital. Calculate the
amount of goodwill of the firm.
a) Rs.85,000
b) Rs.1,00,000
c) Rs.20,000
d) None of the above
On solving the provided question, we can say that by unitary method, Total capital of the firm = Rs. 85,000
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
Heena and Sudha share profits and losses equally.
If the capital of Teena is 1/5 of the total capital which is equal to Rs. [tex]90,000[/tex] 1/5 of Total capital = Rs. [tex]90,000[/tex]
Total capital = Rs. 90,000 × 5 = 4,50,000, capital of all partners = Rs. [tex]1,20,000 + Rs. 80,000 + Rs. 90,000 + 60,000 + Rs. 15,000[/tex]
Total capital of all partners = Rs. [tex]3,65,000[/tex]
Total capital of the firm = Rs. [tex]85,000[/tex]
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A support hotline asks callers to stay on the line after they have completed their call to respond
to a short survey.
Let h(x) = (gof)(x)=√x+3
Which of the following could be a possible decomposition of h(x)?
A. f(x)=√x; g(x)=x+3
B. f(x)=x; g(x)=x+3
c. f(x)=x+3; g(x)=√x
D. f(x)=3x; g(x)=√x
Answer:
the correct answer is letter A
Select the correct answer.
Which statement describes the solutions of this equation?
(X/3) + (x-1/x+4) = (x+3/x+4) help please
The statement describes the solutions of this equation is
The Equation have two valid solution and No Extraneous solution.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
x/3 + (x-1)/ (x+ 4)= (x+3)/ (x+4)
Now, simplifying the above Expression
(x² + 4x + 3x - 3) / 3(x+4) = (x+3)/ (x+4)
(x² + 4x + 3x - 3) / 3 = (x+3)
x² + 7x -3 = 3(x+3)
x² + 7x -3 - 3x - 9 = 0
x² + 4x - 12 = 0
Solving the above Quadratic Equation
x² + 6x- 2x - 12 = 0
x(x+6)- 2(x+6)= 0
(x-2)(x+6)= 0
x= 2, -6.
So, the Equation have two valid solution and No Extraneous solution.
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Required information
[The following information applies to the questions displayed below.]
University Car Wash built a deluxe car wash across the street from campus. The new machines cost $219,000 including
installation. The company estimates that the equipment will have a residual value of $19,500. University Car Wash also
estimates it will use the machine for six years or about 12,500 total hours. Actual use per year was as follows:
Year
123456
Hours Used
2,800
1,400
1,500
2,500
2,300
2,000
Answer:
Step-by-step explanation:
Calculate the total hours used: We add up the hours used each year to find the total hours used:
2,800 + 1,400 + 1,500 + 2,500 + 2,300 + 2,000 = 12,500
Calculate the total depreciation: We subtract the residual value from the cost to find the total depreciation:
$219,000 - $19,500 = $199,500
Calculate the annual depreciation expense: We divide the total depreciation by the number of years to find the annual depreciation expense:
$199,500 / 6 = $33,250
Calculate the depreciation expense per hour: We divide the annual depreciation expense by the estimated total hours to find the depreciation expense per hour:
$33,250 / 12,500 = $2.66
So the depreciation expense per hour is $2.66.
Calculate the depreciation expense for each year: We multiply the hours used each year by the depreciation expense per hour to find the depreciation expense for each year:
Year 1: 2,800 * $2.66 = $7,448
Year 2: 1,400 * $2.66 = $3,724
Year 3: 1,500 * $2.66 = $3,990
Year 4: 2,500 * $2.66 = $6,650
Year 5: 2,300 * $2.66 = $6,118
Year 6: 2,000 * $2.66 = $5,320
So the depreciation expense for each year is:
Year 1: $7,448
Year 2: $3,724
Year 3: $3,990
Year 4: $6,650
Year 5: $6,118
Year 6: $5,320
14. What is the equation of the line that passes through the
point (-3, -5) and has a slope of
-2/3
Answer:
y=-2/3x-0.5
Step-by-step explanation:
y=mx+b is the equation for slopes so I used it and all I needed to find was the y-intercept, which is -0.5
A. 26 square feet
B. 24 square feet
C. 12 square feet
D. 16 square feet
Answer:
The area of the quadrilateral is C: 12 square feet.
Step-by-step explanation:
In the photo, the quadrilateral is divided into two triangles, both having a base length of 4 feet and a height of 3 feet. Therefore, we can find the area of the entire quadrilateral by adding the areas of the two triangles together. Since the triangles have a base length of 4 feet and a height of 3 feet, their individual areas will be [tex]4*3*\frac{1}{2} =12*\frac{1}{2} = 6[/tex] square feet. As there are two triangles, we need to multiply the area of one triangle by 2 to get the total area of the quadrilateral, which would be [tex]6 * 2=12[/tex] square feet. Hence, we can conclude that the correct answer will be C.
Have a great day! Feel free to let me know if you have any more questions :)
Please help me with the quwstion below
Answer:Steve
Step-by-step explanation:
Let
U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.
List all the members of the given set. (Enter your answers as a comma-separated list.)
A ∪ (B ∩ C)
On solving the provided question we can say that The sets are as U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.
what is set?A mathematical representation of a variety of different things is called a set. Any type of mathematical object may be one of the elements or terms that make up a set. Symbols, numbers, lines, other geometric shapes, points in space, variables, and even other quantities. A proposition in mathematics is a structured group of items that can be expressed as a list or a proposition builder. Curly brackets are commonly used to identify sets. For instance, A = 1, 2, 3, 4 is a set. A set is essentially a group of items that are seen together. The items that make up a set are referred to as its members or elements. The components of a set may consist of any item, but for our purposes, they usually consist of mathematical objects like numbers, functions,
The sets are as U = {2, 3, 4, 5, 6, 7, 8}, A = {2, 3, 4, 5}, B = {2, 3, 6, 7}, and C = {4, 6, 8}.
z(180) = (180-185)/4 = -1.25
P(x < 180) = P(z < -1.25)
3)28 C 5
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7. The proof shows that opposite angles of a parallelogram are congruent.
Given: ABCD is a parallelogram with diagonal AC.
Prove: ZBAD ZDCB
Proof:
Statements
ABCD is a parallelogram with diagonal AC.
AB II CD and AD II BC
42 = 23
21 = 24
m22= m23 and m/1 =m24
D
mz1+m22=m24+ m22
m21+ m/2 = m24+ m23
mz1+mz2 = m/BAD
m23+ m24 = m/DCB
m/BAD = m/DCB
ZBAD LDCB
Reasons
Given
Definition of parallelogs
Alternate interior angl
are congruent.
Measures of congru
are equal.
Addition property
Angle addition
Substitution
Angles are c
their measu
What is the missing reason in this partial proof?
?
A. ASA
B. Substitution
C. Angle addition postulate
D. Alternate interior angles are congruent.
The completed two-column table that is used to prove the congruence of ∠BAD and ∠DCB indicates that the missing proof in step 6 of the table is substitution. The correct option is option B
B. Substitution
What are congruent angles?
Congruent angles are angles that have the same measurement,
The two-column table is presented as follows;
[tex]{}[/tex] Statements Reasons
1. ABCD is a parallelogram with diagonal [tex]\overline{AC}[/tex] [tex]{}[/tex] Given
2. [tex]\overline{AB}[/tex]║[tex]\overline{CD}[/tex] and [tex]\overline{AD}[/tex]║[tex]\overline{BC}[/tex] [tex]{}[/tex] Definition of a parallelogram
3. ∠2≅∠3, ∠1≅∠4 [tex]{}[/tex] Alt. int. ∠s are ≅
4. m∠2 = m∠3 and m∠1 = m∠4 [tex]{}[/tex] Measures of ≅ ∠s are =
5. m∠1 + m∠2 = m∠4 + m∠2 [tex]{}[/tex] Addition prop. of equality
6. m∠1 + m∠2 = m∠4 + m∠3[tex]{}[/tex] Substitution
7. m∠1 + m∠2 = m∠BAD [tex]{}[/tex] Angle addition property
m∠3 + m∠4 = m∠DCB
8. m∠BAD = m∠DCB [tex]{}[/tex] Substitution
9. ∠BAD ≅ ∠DCB [tex]{}[/tex] Angles are congruent if [tex]{}[/tex]
[tex]{}[/tex] their measures are the same
The missing reason in the partial proof is therefore; B. Substitution
The abbreviations in the table are expanded as follows;
Alt. int. ∠s are ≅; Alternate interior angles are congruent
Measures of ≅ ∠s are =; Measures of congruent angles are equivalent
Addition prop. of equality; Addition property of equality
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I need help with this math problem please
The scale factor of dilation is 4/9
How to determine the scaled factorFrom the question, we have the following parameters that can be used in our computation:
The triangles
Given that the right is the scaled copy of the left
We have the following representation
Scaled factor = Right/Left
Substitute the known values in the above equation, so, we have the following representation
Scaled factor = 4/9
Hence, the scale factor is 4/9
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Find the future value of an annuity due with a monthly payment of $300 at 6% interest compounded
monthly for 10 years.
O $4117.46
O $49163.80
O $49409.62
$52113.63
O $52374.20
O $109,163.80
Answer: The future value of an annuity due with a monthly payment of $300 at 6% interest compounded monthly for 10 years can be calculated using the formula:
FV = PMT * ( ( (1 + r)^n - 1) / r) * (1 + r)
where PMT = $300, r = 6%/12 = 0.05, and n = 10 years * 12 months/year = 120 months.
Substituting these values into the formula, we get:
FV = $300 * ( ( (1 + 0.05)^120 - 1) / 0.05) * (1 + 0.05)
FV = $300 * ( ( 1.05^120 - 1) / 0.05) * 1.05
FV = $300 * ( ( 2.704813829421526 - 1) / 0.05) * 1.05
FV = $300 * ( 1.704813829421526 / 0.05) * 1.05
FV = $300 * 34.09627658843153 * 1.05
FV = $52,113.63
Therefore, the future value of the annuity due is $52,113.63.
Step-by-step explanation:
Determine the number of monthly payments of $611.09 that would be required to pay off the loan of $128,000 at 4% interest.
The number of monthly payments required to pay off the loan of $128,000 at 4% interest is 232.48 which is equivalent to approximately 232 payments.
How do we determine the number of monthly payments for the loan?To determine the number of monthly payments required to pay off a loan, you can use the formula for loan amortization: n = (-log(1 - B/A * r)) / log(1 + r)
Where: n = number of monthly payments, A = loan amount ($128,000), B = monthly payment ($611.09), r = monthly interest rate (4% / 12 months = 0.0033)
The number of monthly payments for the loan is plugged and computed as:
n = (-log(1 - $128,000/$611.09 * 0.0033)) / log(1 + 0.0033)
n = (-log(1 - 0.0208)) / log(1.0033)
n = (-log(0.9792)) / log(1.0033)
n = 21.8068 / 0.093984
n = 232.48 payment.
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Find the perimeter of the figure.
Answer:
Step-by-step explanation:
its 11
ignore bllllllllllldjbjddddddddddddddddddddddddd
Please help me with this please
Answer:
He will need 64 ft of fencing
Step-by-step explanation:
To determine the amount of fencing, we need to find the perimeter.
P = 2 (l+w) where l is the length and w is the width
P = 2(22+10)
P = 2(32)
P = 64
He will need 64 ft of fencing
Fine Angle R using law of cosines. Round to the nearest tenth
The measure of angle R from the triangle PQR is 15.31°.
What is cosine rule?In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.
The formula for the cosine rule is c=√(a²+b²-2ab cosC)
In the given triangle PQR, PQ=9 units, PR=12 units and RQ=20 units
PQ²=PR²+RQ² -2×12×20cosR
9²=12²+20² -2×12×20cosR
81=144+400-480cosR
81=544-480cosR
81-544= -480cosR
-463= -480cosR
cosR= 463/480
cosR= 0.9645
∠R=15.31°
Therefore, the measure of angle R is 15.31°.
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am a 4-digit number. My thousands digit is greater than 6, but less than 8 My hundreds digits is the highest even number. and ones The sum of my tens cligit a digit is equal to my hundreds digit. My tens digit is 6. Who am I?
Answer:
From the given information, we know that:
The thousands digit is greater than 6 and less than 8, so it must be 7.
The hundreds digit is the highest even number, so it must be 8.
The tens digit is 6.
The sum of the tens and ones digit is equal to the hundreds digit, so 6 + ones digit = 8.
Solving for the ones digit, we get:
ones digit = 8 - 6 = 2
Putting the digits together, we get the number: 7862.
So, the 4-digit number that satisfies all the given conditions is 7862.
Step-by-step explanation:
Given the clues, the thousands digit is 7, the hundreds digit is 8, the tens digit is 6, and the ones digit is 2; therefore, the 4-digit number is 7862.
Explanation:Given the hints, we can infer that:
The thousands digit is greater than 6, but less than 8, so it can only be 7.The hundreds digit is the highest even number, which is 8.The tens digit was specifically said to be 6.The sum of the tens and ones digit is equal to the hundreds digit. The tens digit is 6 and the hundreds digit is 8, so the ones digit must be 2 because 6 + 2 = 8.Therefore, the 4-digit number is 7862.
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Circles and answers please just need help tthank you so mwa
On solving the provided question, we can say that In decimals r = 3.8799 and d = 7.7598
What is decimal?Integer and non-integer numbers are οften expressed using the decimal numeral system. The Hindu-Arabic numeral system has been expanded tο include non-integer values. Decimal notation is the name fοr the method used to represent numbers in the decimal system.
A decimal is a number with a whοle and a fractional component. Decimal numbers, which are in between integers, are used tο express the numerical value οf full and partially whole amounts.
the lengths (in inches) οf the radius and the diameter οf a circle with area 47.25 in'.
Area = πr²
47.25 = 3.14 × r × r
r × r = 15.0541401274
In decimals
r = 3.8799
d = 7.7598
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Find the equation for the line through the point (7/5,1/12) that is perpendicular to the line 3x-4y=7. You may leave your answer in the point-slope form if you wish. If you use slope-intercept form, all fractions must be combined and reduced wherever possible.
The equation of the line is (y - 1/12) = -4/3(x - 7/5).
What is the slope of a line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinates to the change in the x coordinate.
Both the net change in the y-coordinate and the net change in the x-coordinate are represented by y and x, respectively.
Consequently, the formula for the change in the y-coordinate with respect to the change in the x-coordinate is
m = y/x = y/x = change in y/change in x
where "m" represents a line's slope.
Additionally, the slope of the line can be depicted by
tan θ = Δy/Δx
So, the slope of a line is tan.
The given equation of a line is:
3x-4y=7
-4y = -3x + 7
y = 3/4 x - 7/4
The slope of the line is 3/4.
The slope of the line perpendicular to the given line is - 1/m = - 4/3
The point-slope of a line is y - y₁ = m(x - x₁).
The given point is (7/5,1/12)
The equation of the line is
(y - 1/12) = -4/3(x - 7/5)
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A researcher recorded the number of people in each vehicle that passed through a checkpoint. The table above shows the percent distribution for the 420 vehicles that passed through the checkpoint yesterday morning. How many of the 420 vehicles contained at least 3 people?
*
1 point
Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.
Given :
percent distribution : 40% , 35% , 15% , 7% , 3%
Vehicles : 420
First, add the percentage of cars containing 3 people, 4 people, and 5 or more people:
15% + 7% + 3% = 25%
Thus, 25% of the cars contained at least 3 people, so use that to calculate the number of cars:
420 × 0.25 = 105 cars.
Hence , Total 105 of the 420 vehicles contained at least 3 people. Therefore , option C is correct.
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Complete question:
A researcher recorded the number of people in each vehicle that passed through a checkpoint. The table above shows the percent distribution for the 420 vehicles that passed through the checkpoint yesterday morning.
How many of the 420 vehicles contained at least 3 people?
A. 42
B. 63
C. 105
D. 315
Solve for x:
-4x + 2(x+4)= -7x- (x + 1)
Answer: x = -3/2
Step-by-step explanation:
-4x + 2(x+4) = -7x - (x+1)
-4x + 2x+8 = -7x -x-1
-2x + 8 = -8x - 1
+2x +2x
8 = -6x - 1
+1 +1
9 = -6x
/-6 /-6
-9/6 = x
-3/2 = x
