Answer:
5
Therefore, she must get 5 points from the last quiz to have a mean score of 4
Step-by-step explanation:
Mean is the average of a set of data, it is the sum of the data divided by the number of data.
To have a mean of 4 from 4 quizzes;
Let x represent the total;
mean = x/4
4 = x/4
x = 4 × 4 = 16
To have a mean of 4 he must have a total score of 16.
Let y represent her score in the last quiz;
16 = 4+3+4+y
16 = 11+y
y = 16-11 = 5
Therefore, she must get 5 points from the last quiz to have a mean score of 4
The teacher needs to get a score of 5 on her last quiz to have a mean score of 4.
To find out what score the teacher needs on the last quiz to have a mean score of 4, we can use the formula for mean (average):
Mean = (Sum of all scores) / Number of quizzes
Given:
- The teacher has taken 3 quizzes with scores of 4, 3, and 4.
- The mean score she wants is 4.
- Each quiz is worth 5 points.
Let x be the score she needs on the last quiz.
Sum of all scores = 4 + 3 + 4 + x = 11 + x
Number of quizzes = 4 (as she takes 4 quizzes in total)
Now, we can set up the equation and solve for x:
Mean = (Sum of all scores) / Number of quizzes
4 = (11 + x) / 4
4 * 4 = 11 + x
16 = 11 + x
x = 16 - 11
x = 5
Therefore, the teacher needs to get a score of 5 on her last quiz to have a mean score of 4.
What is 8/15÷2/5?What so u think is the best answer for this problem??
Answer:
1 1/3
Step-by-step explanation:
Solve. Change the division sign into a multiplication, and flip the second fraction:
(8/15)/(2/5) = (8/15) x (5/2)
Multiply across:
(8 x 5)/(15 x 2) = (40)/(30)
Simplify. Divide common factors:
(40/30)/(10/10) = 4/3
4/3 or 1 1/3 is your answer.
~
Answer:
1⅓
Step-by-step explanation:
8/15 ÷ 2/5
8/15 × 5/2
(8×5)/(15×2)
4/3
1⅓
a(b+c)=a(c+b)
which property explain why these two expressions are equal?
a) Identity property
b) Symmetric Property
c) associative Property
d) commutative property
Maria bought a swimming pool with a circumference of 24 feet. She wants to buy a cover for her pool. Maria will need to buy _______ square foot pool cover. Use 3.14 for pi.
A. 7.64
B. 11.99
C. 45.82
D. 183.28
Answer:
C. 45.82
Step-by-step explanation:
We know the circumference is given by
C = 2 * pi *r
24 = 2 * 3.14 * r
24 = 6.28r
Divide each side by 6.28
24/6.28 = r
r = 3.821656051
We want to find the area
A = pi r^2
A =3.14 * (3.821656051) ^2
=45.85987261
what’s the answer to this?v
The Pyramid Arena in Memphis, Tennessee is about 98 meters tall
and has a square base with a side length of about 180 meters. A prism-shaped
building has the same square base as the Pyramid Arena. What is the height of
the building if it has the same volume as the Pyramid Arena?
Answer:
Height of the building is 32.67 meters.
Step-by-step explanation:
Volume of a Pyramid = [tex]\frac{1}{3}(\text{Area of the rectangular base})(\text{Height})[/tex]
Side of the square base of the Memphis pyramid = 180 m
Height of the pyramid = 98 meters
Volume = [tex][\frac{1}{3}(180)^2](98)[/tex]
= 1058400 cubic meters
Another building having the same base and volume, is in the shape of a prism.
Therefore, Volume of the pyramid = volume of the building(prism) = 1058400 cubic meters
Volume of the prism = (Area of the base) × height
1058400 = (180)²h
h = [tex]\frac{1058400}{180\times 180}[/tex]
h = 32.67 meters
Therefore, height of the building in the prism shape is 32.67 meters.
Which expression is equivalent to 16a + 24b? (EE1.3)
4(4a + 20b)
8(2a + 3b)
4a(4 + 6b)
8ab(2 + 3)
Final answer:
The equivalent expression to 16a + 24b is 8(2a + 3b) by factoring out the greatest common factor of 8 from both terms.
Explanation:
The expression equivalent to 16a + 24b is 8(2a + 3b). To find this, we can factor out the greatest common factor from the terms in the original expression. Both 16a and 24b have a common factor of 8, which when factored out leaves us with 2a and 3b, respectively, yielding the expression 8(2a + 3b).
45% of the 6th graders at Dutchtown Middle went to the Valentine's Dance. If 126 students went to the dance, how many 6th grade students are there at Dutchtown Middle?
Answer: 280
To find the total number of 6th grade students at Dutchtown Middle, we can set up a proportion based on the information given:
- 45% of the 6th graders went to the Valentine's Dance.
- 126 students attended the dance.
Let us denote the total number of 6th grade students as N.
Given that 45% of the 6th graders is equal to 126 students, we can write the equation as:
(45/100)N = 126
[tex]\[ 0.45N = 126 \][/tex]
[tex]\[ N = \frac{126}{0.45} \][/tex]
[tex]\[ N = \frac{126}{0.45} \]\[ N = 280 \][/tex]
Therefore, the total number of 6th grade students at Dutchtown Middle is 280.
Quita bought a jacket priced at $88. The sales tax rate on the jacket was 7.5%. How much was the sales tax in dollars and cents on this jacket?
Need help !!!
Answer:
i think the answer is 3.3
Step-by-step explanation:
Final answer:
Quita paid $6.60 in sales tax for an $88 jacket.
Explanation:
To calculate the sales tax Quita had to pay for her jacket, we need to follow a simple two-step process.
First, we will calculate the amount of tax by converting the percentage to a decimal and then multiplying it by the price of the jacket.
Since the tax rate is 7.5%, we convert this to a decimal which gives us 0.075.
Then, we multiply this decimal by the price of the jacket:
Amount of sales tax = price × rate of sales tax
$88.00 × 0.075 = $6.60
So, the sales tax on the jacket priced at $88 is $6.60.
Mr. Valdez puts $10,000 in a retirement account and does not make any deposits or withdrawals. The table below shows the amount of money in the account after x years.
A 2-column table with 5 rows. The first column is labeled years with entries 0, 10, 20, 30, 40. The second column is labeled amount (dollar sign) with entries 10,000; 16,000; 27,000; 43,000; 70,000.
What values, rounded to the nearest hundredth, complete the exponential regression equation that models the data?
f(x) =
(
)x
Answer:
The answer on edge. is f(x) = 9,974.73 ( 1.05 )x
Step-by-step explanation
Your Welcome ツ
The value that complete the regression equation is f(x) = 9,974.73 ( 1.05)^x.
How to solve for the value
We have the exponential equation as
[tex]y=ab^{x}[/tex]
a is the initial rate
b is the rate
x is 0
y = 10000
When substituted the rate is given as
f(x) = 9,974.73 ( 1.05 )x
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Which expression can be used to determine the length of segment AB?
Answer:
see explanation
Step-by-step explanation:
Calculate the length using the distance formula
AB = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = A(4,3) and (x₂, y₂ ) = B(- 2, 1)
AB = [tex]\sqrt{(-2-4)^2+(1-3)^2}[/tex]
= [tex]\sqrt{(-6)^2+(-2)^2}[/tex]
= [tex]\sqrt{36+4}[/tex]
= [tex]\sqrt{40}[/tex]
= [tex]\sqrt{4(10)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{10}[/tex] = 2[tex]\sqrt{10}[/tex] ← exact length
Before compairing the price of the different plans, fill in the blanks below for the per minute price, and then add the monthly fee and find the real per minute price.
Plan A - 250 anytime minutes for $30 per month
100min 250min 500min
30$ monthly fee ______ ______ ______
45 cent additional minutes ______ ______ ______
Price per minute ______ ______ ______
Answer:3
Step-by-step explanation:
A sweater was on sale at 40% off the regular price. Ella saved $20 by buying the sweater on
sale. What was the regular price of the sweater?
$40
$80
550
$60
Answer:
$50
Step-by-step explanation:
Sale on sweater = 40% .
Money saved = $20 .
Let original price be x then ,
=> 40% of x = $20
=> 40x/100 = $20
=> x = $20 *100/40
=> x = $ 50
y is directionally proportial to x, when y = 30 and x = 6, work out an equation connecting x and y
Answer:
y = 5x
Step-by-step explanation:
The standard equation for directly proportional equations is y = kx. We can see that y is directionally proportional to x when y = 30 and x = 6 and we need to work out an equation connecting x and y.
→ First step is to substitute in the values
y = k × x
30 = k × 6
→ Divide both sides by 6 to isolate k and find the value of k
5 = k
k = 5
→ Now we substitute k = 5 back into y = kx
y = 5x
Answer:
y=5x
Step-by-step explanation:
The answer is y=5x hope you have a nice day!
Let R1 and R2 are the remainders when the polynomials x^3 + 2x^2 − 5ax − 7 and x^3 + ax^2 − 12x + 6 are divided by x + 1 and x − 2 respectively. If R1+R2 = 6, find the value of a.
Answer:
2.44
Step-by-step explanation:
Given: x³ + 2x² - 5ax - 7 and x³ + ax² - 12x + 6
Also, R1 + R2 = 6
in order to find the value of a:
Let p(x) = x³ + 2x² - 5ax - 7 and q(x) = x³ + ax² - 12x + 6
Using remainder theorem i.e if a polynomial p(x) is divisible by polynomial of form x - a then remainder is given by p(a).
Then,
R1 = p( -1 ) = (-1)³ + 2(-1)² - 5a(-1) - 7 = -1 + 2 + 5a - 7 = 5a - 6
R2 = q( 2 ) = 2³ + a(2)² - 12(2) + 6 = 8 + 4a - 24 + 6 = 4a - 10
Now,
R1 + R2 = 6
5a - 6 + 4a - 10 = 6
9a = 22
a=2.44
Therefore, Value of a is 2.44
A state park has a normally distributed daytime temperatures in the month of June. The mean temperature is 75 Fahrenheit and then standard deviation of 7. What is the probability the temperature is above 82F?
Answer:
0.16
Step-by-step explanation:
This probability is the area under the standard normal curve to the right of 82. Note that 82 is ONE standard deviation above the mean: 75 + 7 = 82.
According to the Empirical Rule, 68% of data lies within one standard deviation of the mean. In other words, 34% lies between the mean and one standard deviation above the mean. The remaining area under the standard normal curve is thus (100% - 68%), or 32%. Half of that is 16%.
The probability that the temperature is above 82, or above 1 standard deviation above the mean, is 16%, which we can also express as 0.16.
Alternatively, use a calculator with built-in statistical functions. In this case the desired result is found by executing the following command:
normcdf(82, 10000, 75, 7). The desired result is 0.1587, or approximately 0.16.
A pair of jeans costs $34.00. You have a coupon for 30% off the regular price. What is the new price of the jeans after you use your coupon?(Hint. This is a two step problem. You will have to multiply and subtract) *
To find the new price of the jeans after using a 30% off coupon, multiply the original price by the discount percentage and subtract that amount from the original price.
Explanation:To find the new price of the jeans after using the 30% off coupon, you need to multiply the original price by the discount percentage and subtract that amount from the original price. Here's how:
Calculate the discount amount by multiplying the original price ($34.00) by the discount percentage (30% or 0.30). The discount amount is $34.00 * 0.30 = $10.20.Subtract the discount amount from the original price to find the new price of the jeans. $34.00 - $10.20 = $23.80.Therefore, the new price of the jeans after using the coupon is $23.80.
NEED HELP ASAP IM ALREADY FAILING ‼️‼️‼️The table below shows the number of miles Alan biked over time. Alan biked at a constant speed. Find the rate of change.
Circletown's limits form a perfectly circular shape. It has a population of 20000 and a population density of 480 people per square kilometer.
What is Circletown's radius?
Answer:
r = 3.64 km
Step-by-step explanation:
Given the following information:
population of the town: 20000 people population density : 480 people per square kilometer=> The area of the town is:
= Total population / population density per square kilometer
[tex]A = \dfrac{20000}{480}[/tex]
[tex]A = 41.667\ km^2[/tex]
As we know, the formula used to find the area of a circle is:
A = π[tex]r^{2}[/tex]
In this situation, we already knew the area of the town
<=> A = π[tex]r^{2}[/tex] = 41.776
<=> [tex]r^{2}[/tex] = 41.776 / 3.14
<=> r = 3.64 km
So the radius of the town is 3.64 km
Answer:
3.64
Step-by-step explanation:
The difference of the square of a number and 18 is equal to 3 times that number. Find
the positive solution.
Answer:
6.
Step-by-step explanation:
To solve this, you can set up an equation as such:
x²-18= 3x
Now, rearrange this to make it an equation in standard form:
x²-3x-18=0.
Simply turn this equation into factored form:
(x-6)(x+3)= 0.
The only positive solution here is x=6.
The problem is about a quadratic equation where a number's square, minus 18 equals 3 times the number. This equation is solved by factoring to get two potential solutions, -3 and 6. The positive solution is 6.
Explanation:The subject matter of this question is quadratic equations in Mathematics. We are to find a number where the difference between the square of the number and 18 is equal to 3 times the number.
We first turn this into a quadratic equation:x2 - 3x - 18 = 0. Then we solve using a technique such as factoring which results to (x - 6)(x + 3) = 0. Giving the solutions x = 6 and x = -3.
Since you asked for the positive solution, x = 6 is the correct answer.
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Find 3 consecutive integers whose sum is 105.
Answer:
34 + 35 + 36 = 105
Step-by-step explanation:
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 105
3X + 3 = 105
3X + 3 - 3 = 105 - 3
3X = 102
3X/3 = 102/3
X = 34
Which means that the first number is 34, the second number is 34 + 1 and the third number is 34 + 2. Therefore, three consecutive integers that add up to 105 are 34, 35, and 36.
34 + 35 + 36 = 105
We know our answer is correct because 34 + 35 + 36 equals 105 as displayed above.
There are 43 students in a classroom with 5
tables. If 8 students can sit at a table, how
many students cannot sit down at tables?
5
Answer:
3
Step-by-step explanation:
8 x 5 = 40
43 - 40 = 3
The number of students who cannot sit at tables based on the given conditions in a classroom setting are 3.
The number of students who cannot sit at tables can be calculated as follows:
Number of students per table = 8
Total number of students = 43
Total number of students that can be accommodated by tables = 5 tables x 8 students = 40 students
Number of students who cannot sit at tables = Total number of students - Total number accommodated by tables = 43 - 40 = 3 students
Which equation demonstrates the multiplicative identity property?
t
O (-3+51)+(--3+5i
O (-3+5)(1)--3+51
O (-3+5)(-3+5)) --16-301
0 (-3+5)(3-5) - 16+301
Answer:
Long story short its C)
Step-by-step explanation:
Option B is correct, (-3 + 5i) (1) = -3 + 5i equation demonstrates the multiplicative identity property
What is Number system?A number system is defined as a system of writing to express numbers.
The multiplicative identity property is a multiplicative property in mathematics where each number multiplied by 1 will produce the original number or can be stated simply :
"The product of any number and one is that number"
So The Multiplicative Identity is 1 can be stated in the formula:
a×1=1×a=a
(-3 + 5i) (1) = -3 + 5i
This is a multiplication operation and 1 is a Multiplicative Identity of multiplication, so the statement is true
Hence, option B is correct, (-3 + 5i) (1) = -3 + 5i equation demonstrates the multiplicative identity property
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A theatre sells two types of tickets to their plays; children’s tickets and adult tickets. For today’s performance they have sold a total of 1180tickets. Also, the have sold 80 more adult tickets than children’s tickets. How many adult tickets have they sold?
Answer:
630
Step-by-step explanation:
Let the number of adult tickets be a.
Let the number of children tickets be c.
For that day's performance, they have sold a total of 1180 tickets. That means that:
a + c = 1180 _____________ (1)
Also, they have sold 80 more adult tickets than children’s tickets.
This means that:
a = c + 80 ______________(2)
Putting (2) in (1):
c + 80 + c = 1180
2c + 80 = 1180
Collecting like terms:
2c = 1180 - 80
2c = 1100
c = 1100 / 2 = 550
From (2):
a = 550 + 80
a = 630
They sold 630 adult tickets.
Final answer:
The theatre has sold 630 adult tickets after solving a system of equations based on the given conditions of total tickets sold and the difference between adult and children's tickets.
Explanation:
The student is presented with a problem where a theatre sells two types of tickets: children's and adult's tickets. For a particular performance, a total of 1180 tickets were sold, and there are 80 more adult tickets sold than children's tickets. We can let 'x' represent the number of children's tickets sold, and thus 'x + 80' will represent the number of adult tickets sold. According to the information given:
x + (x + 80) = 1180
Solving for 'x' we get:
2x + 80 = 1180
2x = 1100
x = 550
Now, to find the number of adult tickets sold, we add 80 to the number of children's tickets.
x + 80 = 550 + 80
x + 80 = 630
Therefore, the theatre has sold 630 adult tickets.
PLEASE PLEASE PLEASE HELP
LOTS OF POINTS
Find the area of the shaded segment of the circle.
Answer:
Around 55.9
Step-by-step explanation:
The first step is to find the area of segment of the circle. Since the segment is a 90 degree angle and a total circle is 360, it is a quarter of the area of a circle. Therefore, you can find its area with the formula [tex]\frac{1}{4}\pi r^2=49\pi[/tex]. Now, you can find the area of the triangle inside. Since all of the radii in a circle are the same length, the triangle has two sides of length 14. Using the triangle area formula, you get an area of 14*14/2=98 square centimeters. [tex]49\pi-98\approx 55.9[/tex] square centimeters. Hope this helps!
Hey! I need help ,
Find the cube root of -27/125
= Cube root of -27 = -3 (because the factors of 27 = 3×3×3)
= Cube root of 125 = 5 ( because the factors of 125 = 5×5×5)
Thus, cube root of -27/125 = -3/5
Answer:
-3/5
Step-by-step explanation:
hello :
- 27 =(-3)^3 and 125= 5^3
-27/125 = (-3)^3 / 5^3 = (-3/5)^3
so : ∛((-3/5)^3 )= -3/5
6 people sharing 40 lbs of gold evenly. How many do they get? Then subtract 1 2/3 from the result of the problem above & simplify completely. Please help cause it's not accepting what I have
Answer: 6
Step-by-step explanation:
Given Data:
Number of people = 6
Amount of Gold to be shared = 40lbs
Subtract 2/3 from your answer.
Therefore
If six people are to share 40lbs of gold evenly
= 40lbs / 6
Divide through by 2
= 20lbs / 3
= 20lbs / 3 - 2/3
= 18/3
= 6
Each person would get approximately 6lbs of gold
Answer:
1. Each individual gets [tex]6\frac{2}{3}lb[/tex] of gold
2. After subtracting by [tex]1\frac{2}{3}[/tex] , the result is 5
Step-by-step explanation:
Given
Size of Gold = 40 lbs
Number of people = 6
Required
1. Proportion of each individual
2. Subtract [tex]1\frac{2}{3}[/tex] from each proportion
1. Proportion of each individual
To calculate how many each individuals get (in other words, the proportion of each individual), we simply divide the total size of gold by the number of people
Mathematically,
[tex]Proportion = \frac{Total}{People}[/tex]
[tex]Proportion = \frac{40}{6}[/tex]
Reduce fraction to lowest term by dividing numerator and denominator by 2
[tex]Proportion = \frac{20}{3}[/tex]
Convert to mixed fraction
[tex]Proportion = 6\frac{2}{3}[/tex]
Hence each individual gets [tex]6\frac{2}{3}lb[/tex] of gold
2. Subtract [tex]1\frac{2}{3}[/tex] from each proportion
This is represented by
[tex]6\frac{2}{3} - 1\frac{2}{3}[/tex]
Convert both fractions to improper fractions
= [tex]\frac{20}{3} - \frac{5}{3}[/tex]
Find LCM of both fractions
= [tex]\frac{20 - 5}{3}[/tex]
Subtract
= [tex]\frac{15}{3}[/tex]
= 5
Hence, after subtracting by [tex]1\frac{2}{3}[/tex] , the result is 5
What is the 18th partial sum of this geometric series 200, 100, 50
Answer:
515
Step-by-step explanation:
Simplify 12 1/3b + 6 2/3 - 10 2/3b
Answer:
1 2/3b + 6 2/3
Step-by-step explanation:
[tex]12\frac{1}{3}b+6\frac{2}{3}-10\frac{2}{3}b[/tex]
Combine like terms:
[tex]1\frac{2}{3}b+6\frac{2}{3}[/tex]
Since you cannot do any more combination or simplification, you are done. Hope this helps!
The simplified form of the given expression is (26-b)/3.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is [tex]12\frac{1}{3}b+6\frac{2}{3}-10\frac{2}{3}b[/tex].
Here, [tex]12\frac{1}{3}b-10\frac{2}{3}b+6\frac{2}{3}[/tex]
= (36+b)/3 - (30+2b)/3 +20/3
= (36-30+b-2b)/3 +20/3
= (6-b)/3+20/3
= (6-b+20)/3
= (26-b)/3
Therefore, the simplified form of the given expression is (26-b)/3.
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WILL GIVE BRAINLIST PLZZZ HELPPP
Milton got a paperweight like the one shown below. He needs to fill it with sand to give it weight.
If a = 3 inches, what is the volume of the paperweight?
A.
54 cubic inches
B.
81 cubic inches
C.
108 cubic inches
D.
126 cubic inches
Answer:
B. 81 cubic inches
Step-by-step explanation:
Since this is an irregular 3 dimensional object, I will cut it into a 3 by 3 by 3 cube and a 6 by 3 by 3 rectangular prism.
Solving for the cube:
3*3*3=
9*3=
27 units or in this case inches³
Solving for the rectangular prism:
6*3*3=
18*3=
54 units or in this case inches³
To get the total volume, we need to add the cube and rectangular prism's volume together:
54+27=81 inches³
Our answer is B. 81 cubic inches.
The cut wedge represents one-eighth of the cheese. A. Find the surface area of the cheese before it is cut in terms of π ,rounded to the nearest whole number, and as a decimal, round to the nearest tenth. The surface area of the cheese before it is cut is π , or about in.2 2 . B. Find the surface area of the remaining cheese after the wedge is removed. Round the estimated portion of the answer to the nearest whole number. The surface area of the remaining cheese after the wedge is removed is about square inches. Question 2 Did the surface area increase, decrease, or remain the same? Response - correct The surface area decreased.
Answer:
A. The surface area of the cheese is 24·π in.² or 75.40 in.²
B. The surface area of the remaining cheese after the wedge is removed is about 72 in.²
2. The surface area decreased
Step-by-step explanation:
From the figure attached to a similar question, we have;
Radius, r of cheese = 3 in.
Height, h of the cheese = 1 in.
A. The surface area of the cheese is equal to the area of two circles, one on top and the other underneath added to the surface area of the sides which is equivalent to the surface area of a cylinder given by the relation
Surface area of the cheese = 2×π×r² + 2×π×r×h
∴ Surface area of the cheese = 2×π×3² + 2×π×3×1 = 24·π in.²
Surface area of the cheese = 24·π = 75.398 ≈ 75.40 in.² to the nearest 10th
B. The surface area of the remaining cheese after the wedge is removed is found by first subtracting the cut wedge from the total surface area as follow
Outer surface area of cut wedge = 24·π÷8 = 3·π
New outer surface area = Total surface area - Removed outer surface area
∴ New outer surface area = 24·π - 3·π = 21·π
New total surface area = New outer surface area + Area of newly exposed segment
Area of newly exposed segment = 3 × 1 × 2 = 6 in.²
∴ New total surface area = (21·π + 6) in.² = 71.9734 in.² ≈ 72 in.²
The surface area of the remaining cheese after the wedge is removed is about 72 in.²
2. The surface area decreased.
Answer:
A. The surface area of the cheese is 24·π in.² or 75.4 in.² B. The surface area of the remaining cheese after the wedge is removed is about 72 in.² 2. The surface area decreased
Step-by-step explanation:
It's 75.4 instead of 75.40, thank me please.