There are 13340783196 ways to allocate marks to the questions.
It is given that the exam has 12 problems.
There are 11 questions that need to be assigned at least 5 marks while the last answer needs to be assigned at least 10 marks.
Hence the least marks to be assigned
= 11 X 5 + 10
= 65.
Hence are left with assigning 35 marks.
here,
n = 12
r = 35
In this type of problem, we need to use the formula
C(n + r -1 , r)
= ⁴⁶C₃₅
= 46! / (35! X 11!)
Hence no. of way to assign marks
= 13340783196 ways.
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Gary is forming capture the flag teams out of all of the students that signed up from two classes. Each team must have the same number of players and be from the same class. What is the largest number of players that gary can put on each team?.
In the kickball teams, Lee has the ability to put nine players on each team.
What does "greatest common factor" (GCF) mean?
The common number that each term in a group of terms shares, also known as the greatest common factor (GCF), is
All of the students who signed up for kickball teams from two classes are being put together into teams by Lee.
45 students from the one school have signed up to play on the kickball team. Let compose this number in factor structure as,
45 = 3*3*5
because both numbers contain the number three twice. Therefore, GCF = 3*3 GCF = 9 is the greatest common factor of two numbers.
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Full Question = Lee is forming kickball teams that include all of the students who signed up from two schools. Each team must have the same number of players and be from the same school. 45 students from the one school have signed up to play on the kickball team. What is the greatest number of players Lee can put on each team?
What happens after you dilate?
After you dilate a figure , The figure gets bigger or smaller.
Dilation in mathematics is a process of changing the size of an object or a shape without changing its shape.
When you dilate any figure distance between the points changes.
Either the image gets enlarge or shrinks depends on the scale factor.
Things that don't changes are:
Each angle of the figure is the sameMidpoints of the sides of the figure remain the same as the midpoint of the dilated shapeParallel and perpendicular lines in the figure remain the same as the parallel and perpendicular lines of the dilated figureThe images remain the sameOnly the size of an image changes not it's shape.
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Cathy takes out a $167,000 mortgage. She plans monthly payments to pay it off in 40 years. At the end of the term, Cathy will have paid $401,294.40 total. Choose the appropriate APR formula.
APR=2nf/P(N+1)
APR=24(234,294.4)/167,000(481)
APR=2(12)(401,294.4) / 167,000(480+1)
APR=2(12)(167,000)(401,294.4)⋅481
APR=24(284,147.2)401,294.4(480+1)
Cathy takes out a $167,000 mortgage. She plans monthly payments to pay it off in 40 years. At the end of the term, Cathy will have paid $401,294.40 total. The appropriate APR formula is APR=2(12)(401,294.4) / 167,000(480+1)
Define APR.The annual interest produced by a sum that is paid to investors or charged to borrowers is referred to as the annual percentage rate (APR). APR is a percentage that expresses the actual annual cost of borrowing money throughout the course of a loan or the revenue from an investment. This does not account for compounding and includes any fees or additional expenditures related to the transaction. Consumers can evaluate lenders, credit cards, or investment goods using the APR as a benchmark figure.
Given,
Mortgage = $167000
Monthly plan = 40 years
End of the term, Cathy will have paid $401,294.40 total.
APR=2nf/P(N+1)
APR=2(12)(401,294.4) / 167,000(480+1)
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25 points :)))))
2+2x3
Answer:
8
Step-by-step explanation:
2+2x3
1. Use pemdas to do it
8
(40 points awarded for solving) The quadratic function f(x) has roots of 4 and −6, and it passes through the point (1, 21). What is the vertex form of the equation of f(x)?
f(x) = −(x − 1)2 + 25
f(x) = −(x + 1)2 + 25
f(x) = (x − 1)2 + 25
f(x) = (x + 1)2 − 25
The vertex-form definition of the quadratic function is given as follows:
f(x) = −(x + 1)² + 25.
How to define the quadratic function?The roots of the quadratic function are defined as follows:
-6 and 4.
Hence the definition of the function is given as follows:
f(x) = a(x + 6)(x - 4)
f(x) = a(x² + 2x - 24).
When x = 1, y = 21, hence the leading coefficient a is obtained as follows:
21 = a(1 + 2 - 24)
-21a = 21
a = -1.
Thus the standard definition of the function is of:
y = -x² - 2x + 24.
The coefficients of the function are of:
a = -1, b = -2, c = 24.
Then the x-coordinate of the vertex is of:
x = -b/2a = 2/-2 = -1.
The y-coordinate of the vertex is of:
y = -(b² - 4ac)/4a = -((-2)² - 4(-1)(24))/-4 = 25.
Meaning that the vertex-form definition of the quadratic function is of:
f(x) = −(x + 1)² + 25
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Answer: B is the answer i got it right on the test
Step-by-step explanation:
The distribution of heights in a population of women is approximately normal. sixteen percent of the women have heights less than 62 inches. about 97.5% of the women have heights less than 71 inches.
Use the empirical rule to estimate the mean and standard deviation of the heights in this population.
Mean and standard deviation of the height of the population using empirical rule is equal to 65inches and 3 inches.
As given in the question,
Distribution of height in women population:
Percent of women heights less than 62inches = 16%
As per Empirical rule of normal distribution,
It is less than 68% it comes in first standard deviation
μ - σ = 62 __(1)
Percent of women heights less than 71 inches = 97.5%
As per Empirical rule of normal distribution,
It is in the range of 97.5% it comes in second standard deviation
μ +2σ = 71 __(2)
Solve (1) and (2) we get,
μ - σ = 62
μ +2σ = 71
0 - 3σ = -9
⇒ σ = 3inches
⇒ μ = 62 + 3
= 65inches
Therefore, the using empirical rule the mean and standard deviation to represent the height of population is equal to 65inches and 3 inches respectively.
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nt
P(1 + 1) ht
Formula: A = P
Solve the problem by answering the following questions:
An initial investment of $5575 is appreciated for 12 years in an account that earns 3.25%
interest, compounded semiannually. Find the amount of money in the account at the end
of the period.
i. What does each of these variables represent:
The amount of investment will be $8183.24 after compound interest.
What is Compound interest?Compound interest is defined as interest paid on the original principal and the interest earned on the interest of the principal.
A = P(1+r/100)ⁿ
Where:
A = the future value of the investment or loan
P = the principal investment or loan amount
r = the interest rate (decimal)
n = the number of compound periods
As per the question, an initial investment of $5575 is appreciated for 12 years in an account that earns 3.25% interest, compounded semiannually.
The compounded amount will be calculated as:
A = 5575 ( 1 + 0.0325 )¹²
A = 5575 × 1.4678
A = $8183.24
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The table below shows that the number of miles driven by Lydia is directly
proportional to the number of gallons she used.
Gallons Used Miles Driven
42
47
50
1591.8
1781.3
1895
If m represents the number of miles driven for any number of gallons used, g,
write a proportional equation for m in terms of g that matches the context.
how many integer values of x are there so that x, 5, and 8 could be the lengths of the sides of a triangle?
The integer value of x is 6.
What is a side of a triangle?
The three vertices of a triangle connect the straight lines that make up its sides. In other terms, we can state that a triangle's sides are line segments that converge at the triangle's vertices.
Here, we have
Given,
the lengths of the sides of a triangle are x, 5, and 8.
x² + 5² < 8²
x² + 25 < 64
x² < 39, now perfect squares less than 39 are 36, 25, 16, 9, 4, 1.
x² + 5² = 8²
x² + 25 = 64
x² = 39, No integer values.
x² + 5² > 8²
x² + 25 > 64
x² + > 39
Here the possible integer values are infinite.
Hence, the integer value of x is 6.
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in estimating a population proportion using a large sample, the value of is assumed to be 0.35, and its 95% error margin is 0.02. find the sample size to meet the error margin.
2185 people make up the sample size.
What is proportion?
An equation in which two ratios are made equal is called a proportion. For instance, you could write the ratio as 1: 3 (for every one boy, there are three girls), which means that 14 of the population is made up of boys and 34 of the population is made up of girls.
The formula used to determine sample size (n) is as follows:
n = p(1 - p) (z²/ e² )
Where z = 1.96 with a 95% confidence interval (), p is the proportion, and e is the margin of error.
z = 1.96, p = 0.35, e = 0.02
n = 0.35(1 - 0.35) (1.96²/ 0.02²)
n = (0.2275)(9604)
= 2184.91
n ≈ 2185
2185 people make up the sample size.
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if i have 29 pencils and i give 13 away to my friend how much pencils do i have left?
If you have 29 pencils and gave 13 away to your friend, you subtract what you gave away from what you have.
[tex]29-13\\=\fbox{16}[/tex]
Mrs. Robinson bought a novel at the bookstore on sale for 20% off its regular price of $29.99. Mr. Chang bought the same novel at a different bookstore for 10% off its regular price of $25. which person received the better discount? Explain.
Answer: Mrs. Robinson
Step-by-step explanation:
Let's find Mrs. Robinson first
100% - 20% = 80% or 0.8
29.99 times 0.8% = $24
29.99 -24 = $5.99 off
Now Let's find Mr.Chang
100% - 10% = 90% or 0.9
25 times 0.9% = $22.50
25 - 22.50 = $2.50 off
So Mrs. Robinson received a better discount!
What is the equation of a line that contains point(-2,8) and has a slope of two
Equation of the line having passing point (-2,8) and has a slope of 2 is 2x - y + 12 = 0
What is the equation of the line?
A straight line's equation is y = mx + c, c is the height at which the line crosses the plane, and m is the gradient. y -axis, often known as the y -intercept. The gradient m is the slope of the line, which is the percentage increase in the y-coordinate relative to the x-coordinate.
Given:
Passing point of line , (-2,8)
Slope of the line = 2
Equation of the line having passing point (a,b) and slope m become
y - b = m (x - a)
Equation of the line ⇒ y - 8 = 2(x + 2)
⇒ y - 8 = 2x + 4
⇒ 2x - y + 4 + 8 = 0
⇒ 2x - y + 12 = 0
Therefore, equation of the line having passing point (-2,8) and has a slope of 2 is 2x - y + 12 = 0.
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Complete Question
What is the equation of a line that contains point(-2,8) and has a slope of 2?
1/2x 3/4 in the simplest form?
(3, 5), (-3, r), m = 3/4
Answer:
(35),(−3r),m=34(35),(−3),=3/4
Step-by-step explanation:
A sheet of 28 stickers has stars and heart stickers. There are 16 heart stickers. How many heart stickers does a pack of 140 stickers have?
To find the number of heart stickers in a pack of 140 stickers, we can use proportions. We can set up the proportion by using the number of stickers on the sheet of 28 stickers as the denominator and the number of heart stickers on the sheet of 28 stickers as the numerator. The proportion will look like this:
Copy code
(heart stickers in a pack of 140 stickers) / 140 = 16 / 28
To solve for the number of heart stickers in a pack of 140 stickers, we can first multiply both sides of the equation by 140 to get rid of the denominator on the left side:
(heart stickers in a pack of 140 stickers) = 140 * 16 / 28
Then, we can simplify the expression on the right side by dividing the numerator and denominator by 4 to get:
(heart stickers in a pack of 140 stickers) = 35
Therefore, a pack of 140 stickers would have 35 heart stickers.
The lengths of a rectangle have been measured to the nearest tenth of a centimetre.
The upper bound for the area is 4527.7056 cm² and the lower bound for the perimeter is 278 cm.
Area (upper bound) = 4527.7056 cm²
Perimeter (lower bound) = 278 cm
The length and width of the rectangle have been ROUNDED to the nearest tenth. Let's calculate what their actual measurements could be:
LENGTH: rounded to 87.3, actual is between 87.25 and 87.34
87.25 is the lowest number it could be that would round it UP to 87.3
87.34 is the highest number it could be that would round DOWN to 87.3
WIDTH: rounded to 51.8, actual is between 51.75 and 51.84
51.75 is the lowest number it could be that would round it UP to 51.8
51.84 is the highest number it could be that would round DOWN to 51.8
To find the Area of the upper bound, multiply the highest possible length and the highest possible width:
A = 87.34 × 51.84 = 4527.7056
To find the Perimeter of the lower bound, calculate the perimeter using the lowest possible length and the lowest possible width:
P = 2(87.25 + 51.75) = 278
The region is the quantity that expresses the volume of an area at the aircraft or on a curved floor. The vicinity of a plane region or aircraft place refers to the area of a shape or planar lamina, at the same time as floor region refers to the region of an open surface or the boundary of a 3-dimensional object. location may be understood as the quantity of material with a given thickness that might be necessary to style a version of the shape, or the quantity of paint important to cover the surface with an unmarried coat. it's far the 2-dimensional analog of the length of a curve (a one-dimensional idea) or the extent of a stable (a three-dimensional idea).
The area of a shape can be measured by means of comparing the shape to squares of a hard and fast size. inside the worldwide system of devices (SI), the usual unit of the region is the square meter (written as m2), which is the region of a square whose sides are one meter long. A form with a place of three rectangular meters might have an equal area as 3 such squares. In arithmetic, the unit rectangular is described to have placed one, and the region of any other shape or floor is a dimensionless actual quantity.
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Complete question: -
The lengths of a rectangle have been measured to the nearest tenth of a centimeter they are 87.3cm and 51.8cm what is the upper bound for the area and the lower bound for the perimeter
chase looks around at an assembly. He noticed his younger sister to his right and his older brother 16 feet ahead of him. If Chase’s brother and sister are 20 feet apart, how far apart are chase and his younger sister
The distance between Chase and his younger sister is 12 feet. This is calculated by using Pythagoras' theorem.
What is Pythagoras' theorem?The theorem that states "the square of the hypotenuse of a right triangle is equal to the sum of the squares on its other two sides" is said to be Pythagoras' theorem.
I.e., hyp² = opp² + adj²
Calculation:It is given that,
Chase looks around at an assembly. He noticed that his younger sister was to his right and his elder brother is 16 feet ahead of him.
Chase's brother and sister are 20 feet apart, then the distance between Chase and his younger sister forms a right triangle as shown in the figure.
Where SB = 20 feet; CS = X feet; and CB = 16 feet;
According to the Pythagoras theorem, the distance between Chase and his sister is
SB² = CS² +CB²
⇒ (20)² = (x)² + (16)²
⇒ 400 = x² + 256
⇒ x² = 400 -256 = 144
⇒ x = √144 = 12
Therefore, the distance between Chase and his younger sister is 12 feet.
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How do you solve a linear function problem?
The process to solve the linear function problem is explained below .
In the question ,
we have been asked how can we solve a linear function problem .
we know that A linear function is a function that represents a straight line in the coordinate plane.
For Example, let the linear function problem be f(x) = 3x - 2 ,
Step(1) :
to solve it we first have to equate the function to 0 ,
that is 3x - 2 = 0
Step(2) ;
we need to perform the necessary mathematical operation to find the value of x .
adding 2 on both sides of equation 3x - 2,
we get ,
3x = 2
dividing both sides by 3 ,
we have , x = 2/3 ,
the solution is x = 2/3 .
Therefore , the steps to solve a linear function is mentioned above .
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Use the quadratic formula to solve the quadratic equation 2x²-3x -4 = 0.
Separate multiple solutions with commas if necessary.
Answer:
Step-by-step explanation:
4m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/84m-3/4=-9+4m/8
Answer:
[tex]\frac{-3+\sqrt{23} }{4} , - \frac{3+\sqrt{23} }{4}[/tex]
Step-by-step explanation:
quad formula= [tex]x=\frac{b+/-\sqrt{b^{2} -4(a)(c)} }{a^{2} }[/tex]
in your case the [tex]2x^{2}[/tex] is a
[tex]-3x[/tex] is b
and [tex]-4[/tex] is c
and plug it in a calculator twice, add the first time and subtract the second time.
I need this asap I really don’t know what to do lol
What are 3 ways to solve equations?
The three ways of solving equations are graphing substitution and elimination.
To solve an equation by graphing, you essentially chart the given equations and discover the point(s) where they all meet. The arrangement of this point will grant you the values of the factors that you simply are tackling. The following method is substitution. Substitution is best utilized when one of the conditions is in terms of one of the factors such as y=2x+4, but the equations can continuously be manipulated. The primary step in this method is to solve one of the equations for one variable. Once an expression for the variable is found, substitute or plug within the expression into the other equation where the initial variable was to solve for the number esteem of the next variable. The final step is to substitute the number esteem that was found for its comparing variable within the original condition. The third method is the elimination, which involves adding the equations together in arrange to make an equation with as it were one variable. This will was done when the coefficients of one variable in both equations are alternate extremes and will cancel each other out once added together.
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in a college student poll, it is of interest to estimate the proportion p of students in favor of changing from a quarter-system to a semester-system. how many students should be polled so that we can estimate p to within 0.09 using a 99% confidence interval? no information is available concerning an approximate value of p.
Total 205 students should be polled so that we can estimate p to within 0.09 using a 99% confidence interval.
We have given that
Estimate of the proportion of students
= p
Confidence interval = 99%
As we know that the margin of error for the confidence interval is ,
MOE = Z ×√(p × (1-p)) / n
Where Z is z-score for
p --> estimate proportion confidence interval
n --> sample size
margin of error = 0 .09,
so we can set the equation as,
0.09 = Z×√(p×(1-p)) / n
Using the Z-table , the Z value for a 99% confidence interval is 2.575..
we will use p = 0.5 (since we are not given any information about value of p).
plugging all known values in above formula we get, 0.09 = 2.575√(0.5(0.5))/n
=> 0.0349 = √0.25/ n
=>0.00122 = 0.25/n
=> n = 204.6489
Since we get a decimal and we need our answer in number of students to sample, we round up to n = 205.
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HEELLPPP!!!!! An import/export business marks up imported merchandise by . If a wicker chair imported from Singapore originally costs from the manufacturer, what is the retail price?
The retail price is $?
.
The retail price is $354.65.
What is retail price?
The price at which a product's manufacturer ostensibly recommends that a retailer sell it is referred to as the list price, also known as the manufacturer's suggested retail price, recommended retail price, or suggested retail price of a product.
Given: An import/export business marks up imported merchandise by 105%.
A wicker chair imported from Singapore originally costs from the manufacturer $173.
We have to find the retail price.
Retail price = [tex]= 173 + 173*\frac{105}{100} \\[/tex]
= 173 + 181. 65
Retail price = 354.65
Hence, Retail Price is $ 354.65.
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Find the difference between (1.1 × 108) and (4.3 × 107). Write the final answer in scientific notation.
−3.2 × 101
3.2 × 10−1
6.7 × 107
6.7 × 108
The difference between the numbers 1.1 × 10⁸ and 4.3 × 10⁷ will be 6.7 × 10⁷. Then the correct option is C.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
The numbers are given below.
1.1 × 10⁸ and 4.3 × 10⁷
Then the difference between the numbers 1.1 × 10⁸ and 4.3 × 10⁷ will be given by putting a minus sign between them. Then we have
⇒ 1.1 × 10⁸ - 4.3 × 10⁷
⇒ 11 × 10⁷ - 4.3 × 10⁷
⇒ 6.7 × 10⁷
The contrast between the numbers 1.1 × 10⁸ and 4.3 × 10⁷ will be 6.7 × 10⁷. Then, at that point, the right choice is C.
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What is the vertex of the graph of the function f(x)=x^2+8x
Answer:
Step-by-step explanation:
o find the vertex of f(x)=x2−8x+7 , there are several things you can do. You could complete the square to get the equation into vertex ...
Two cubes of volumes $8 \text{~cm}^3$ and $27 \text{~cm}^3$ are glued together at their faces to form a solid with the smallest possible surface area. What is the number of square centimeters in the surface area of the resulting solid?.
The surface area of the resulting solid is 40 cm².
A cube is a three-dimensional figure that has 6 faces and 12 edges and 8 vertices. All of the edges of a cube are of the same length.
If the volume of each of the two cubes is 8 cm³, then the length of its edge is 2 cm.
V = e³
8 = e³
e = 2 cm
Two cubes are glued together. Either side by side or put on top of each other, the dimension of the resulting solid is 4 cm by 2 cm by 2 cm.
Hence, the surface area of the resulting solid is
SA = 2lw + 2lh + 2wh
SA = 2(4 cm)(2 cm) + 2(2 cm)(2 cm) + 2(4 cm)(2 cm)
SA = 40 cm²
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Aaron's dad has a pickup truck and his mom has an SUV. Last week, his dad traveled 84 miles in the pickup truck on 4 gallons of gas. His mom traveled 72 miles in the SUV on 3 gallons of gas. How many more miles per gallon did the SUV get than the truck?
Write your answer as a decimal or a whole number.
Answer:
To find out how many miles per gallon the truck got, we can divide the number of miles it traveled by the number of gallons of gas it used: 84 miles / 4 gallons = <<84/4=21>>21 miles/gallon.
To find out how many miles per gallon the SUV got, we can divide the number of miles it traveled by the number of gallons of gas it used: 72 miles / 3 gallons = <<72/3=24>>24 miles/gallon.
To find out how many more miles per gallon the SUV got than the truck, we can subtract the number of miles per gallon the truck got from the number of miles per gallon the SUV got: 24 miles/gallon - 21 miles/gallon = <<24-21=3>>3 miles/gallon.
The SUV got 3 more miles per gallon than the truck.
Step-by-step explanation:
Answer:The SUV got 3 more miles per gallon than the truck.
Step-by-step explanation:
-20 divided by -5
answer correctly and asap and I will give brainliest
Answer:
4
Step-by-step explanation:
negative divided by a negative is a positive
Write
45 in expanded form.
Answer:
4 x 10 + 5 x 1
Step-by-step explanation:
The expanded form of a number is written as a sum where each digit of the number is multiplied by its place value. Let's understand this concept with an example. To write the number 45 in the expanded form, we split the digits into tens and ones and write it as 4 x 10 + 5 x 1.
Answer:
Step-by-step explanation:
45 in expanded form;
(4x10)+(1x5)= 45