Answer: 0.6375
Step-by-step explanation:
Let's assume that the event that she'll make the first shot is given as P(A) while making the second shot is P(B). Therefore, P(A/B) = 0.85
Therefore, the probability that she makes both free throws will be denoted as:
= 0.75 × 0.85
= 0.6375
Find the greatest common factor (GCF) of 18 and 6 .
GCF=
use the gcf to factor 18 + 6 = _ x (_+_)
The greatest common factor of 18 and 6 is 6
What is Greatest common factor?The greatest common factor is defined as the largest number that is a factor of two or more numbers. For example, the GCF of 24 and 36 is 12, because the largest factor that is shared by 24 and 36 is 12. 24 and 36 have other factors in common, but 12 is the largest.
To find the greatest common factor between 18 and 6, we have to find the common factors of 28 and 6
The factors of 18 are: 1, 2,3,6,,9,18
The factors of 6 are: 1,2,3,6
The common factors are: 1,2,3,6
the greatest common factor is 6
Therefore the greatest common factor of 18 and 6 is 6
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Which of the following is a factor of (x+y)³ - (x³+y³) ?choose the correct answerx²+xy²+2xyx²+y²-xyxy²3xy
The factor of (x + y)³ - (x³+y³) is 3xy is a factor of the given expression.
Factor of Expression:
The factor is part of the product. Both are factors of this term 5y because 5y represents 5 × y and 5 is multiplied by y to form 5y. Expressing a term as the product of two or more variables or numbers is called factorization. Sometimes we need to factorize arbitrary algebraic expressions. For example, y2 + y is factored as y(y+1). This means that y and y+1 are factors of y2 + y and a2- b2 = (a + b)(a - b). That is, (a + b ) and ( a-b) are factors of a² - b².
As we know,
(a + b)³ = a³ + b³ + 3a²b + 3ab²
The given expression can be simplified as,
(x + y)³ - (x³ + y³) = ( x³ +y³ +3x²y + 3xy³) - (x³ +y³)
⇒ (x + y)³ - (x³ + y³) = x³ +y³ +3x²y + 3xy³ - x³ - y³
This gives,
(x + y)³ - (x³ +y³) = 3x²y+ 3xy²
This can be written as,
(x + y)³ - (x³+y³) = 3xy(x + y)
Therefore, we can say that 3xy is a factor of the given expression.
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Triangle abc is congruent to triangle edf. So, priya knows that there is a sequence of rigid motions that takes abc to edf.
Triangle abc is congruent to triangle edf. So, priya knows that there is a sequence of rigid motions that takes abc to edf. From the rigid transformation that takes ABC to EDF, the coinciding parts based on congruency; are matched below.
Triangle congruence is when two triangles are said to be congruent to one another, it signifies that their corresponding sides and angles are equal.
Consequently, we can state that if triangle ABC and triangle EDF are congruent;
Angle A ≅ Angle E
Angle B ≅ Angle D
Angle C ≅ Angle F
Segment AB ≅ Segment ED
Segment AC ≅ Segment EF
Segment BC ≅ Segment DF
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Jenna earns $10.75 per hour working at the mall. If Jenna worked 23 4/5 hours last week, how much did she earn before taxes were taken out?
The total weekly earnings of Jenna before the taxes were taken out is
$255.85.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Jenna earns $10.75 per hour working.
She worked a total of [tex]23\frac{4}{5}[/tex] hours last week.
Therefore, The total earnings of Jenna can be obtained by multiplying her rate per hour by the total number of hours she worked which is,
= 10.75×119/5.
= 10.75×23.8.
= $255.85.
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Question
Juanita borrowed $7,000 interest free from her mother to buy a car. Juanita pays back $150 per month to her mother. How much will she still owe after 2 years of payments?
Answer: $3,400
Step-by-step explanation:
Juanita owes $7,000, she pays $150 a month for two years.
Step 1: Create an equation we can plug our values into
7,000=150x +b ------> x=# of months --------> b=what is still owed
There are 12 months in a year. 12(2)=24
7,000=150(24)+b
7,000=3600 +b
-3600 -3600
$3,400=b
What are the factors affecting substitution reaction?
The factors affecting substitution reaction are Steric nature of the substrate, Nature of nucleophile, Solvent used, Leaving group.
Steric nature of the substrate - The substrate's electrophilic center's steric accessibility is likely the most crucial determinant in determining whether a nucleophilic substitution will follow a Sn1 or a Sn2 mechanism.Nature of nucleophile -Small nucleophiles are preferred by Sn1 and Sn2 reactions.Solvent used - As was already noted, low to moderate polarity solvents like acetone and N,N-dimethylformamide are preferred for Sn2 mechanisms (DMF).Leaving group - The most crucial thing to keep in mind in this regard is that strong bases make ideal departing groupings.To learn more about substitution here:
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How do you construct a dilation with a scale factor of 2?
To construct a dilation with a scale factor of 2, you need graph paper, a compass, a ruler, a straightedge, and a pen/pencil. Sketch the pre-image, measure the distance, construct the centre, draw a line segment and use a compass to draw an arc to construct the image.
To construct a dilation with a scale factor of 2, you will need the following materials:
RulerCompassStraightedge (such as a protractor or triangle)Graph paper Pen or pencilSteps:
Start by sketching the original figure on graph paper. This will be the "pre-image."Use the ruler to measure the distance between two points on the pre-image. This distance will be used to determine the scale factor. Next, use the compass to construct a centre of dilation (also called the "centre of scale") on the pre-image. This can be any point within the pre-image. Using the straightedge, draw a line segment from the centre of the dilation to one of the points on the pre-image. This line segment represents the radius of the dilation.Use the compass to set the radius to twice the length of the line segment from step 4. This creates a scale factor of 2. Use the compass to draw an arc from the centre of the dilation to the pre-image point. This creates the image of dilation.Repeat steps 4-6 for all other points on the pre-image to construct the entire image of the dilation.It's important to note that, the dilation will keep the same shape as the original figure but it will be twice as large as the original figure.
Also, the centre of dilation is the point that stays the same distance from all the points on the image and the pre-image.
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Danielle invested £2800 for n years in a savings account.
She was paid 2.5% per annum compound interest.
The interest is paid into the account at the end of each year.
At the end of n years, the amount of money in the savings account is greater than £3000 for the first time
Work out the value of n.
(Total for question = 2 mar
Therefore , the solution of the given problem of interest comes out to be
time = 3 years.
What is a interest?Simple interest is determined by summing the principal, interest rate, time frame, and other elements. The simple return is determined by dividing the principal by the interests rate along with the number of hours. The easiest way to calculate interest is with this formula. Interest is often determined as a percentage of a principal amount. He would only have to pay 50% of a 100% charge if he asked a buddy for a $100 loan and agreed to repay it with 5% interest. $100 (0.05) = $5. You should pay interest on the money you borrow, and you must add interest to any money you lend.
Here,
=>start * multiplier^t
=> multiplier = 1 + x % = 1.025
try n=1,
n=2,
n=3
So,
2800 * 1.025^n =3000
On comparing n=1,2,3
We get,
2800 * 1.025^3 = 3000
Thus , n=3 is the correct answer.
Therefore , the solution of the given problem of interest comes out to be
time = 3 years.
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Kyle is a salesman. His monthly earnings include a fixed monthly salary and a commission that is a fixed percentage of his total sales for the month.
- Kyle's total sales for the month of January were $15,000 and his total earnings for hat month were $2,550.
- Kyle's total sales for the month of February were $25,000 and his total earnings for that month were $3,050.
What is Kyle's fixed monthly salary in dollars?
Kyle's fixed monthly salary in dollars $1800 and fixed percentage of his total sales for the month is 5%.
What is fixed salary?Fixed pay, also known as a fixed salary, is the predetermined and set sum that an employer pays to a worker at the conclusion of each payroll cycle. The term "fixed pay" refers to all compensation that the company guarantees, most frequently in the form of a monthly or annual salary.
We let his fixed monthly salary be x & his fixed percentage be y so our equations will be:
2,550 = x + 15,000y
3,050 = x + 25,000y
Subtract the equations
3,050 = x + 25,000y
- 2,550 = x + 15,000y
500 = 10,000y
y = 10000/500
y = 0.05 or 5%
Potting the value of in first equation we get,
2,550 = x + 750
x = 2,550 - 750
x = $1800
Thus, Kyle's fixed monthly salary in dollars $1800 and fixed percentage of his total sales for the month is 5%.
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Solve the following equation for F.
√gF+H = u
Therefore , the solution of the given problem of quadratic equation comes out to be F = u²/g −H/g.
Describe a quadratic equation.A quadratic algebraic in a single variable x2+ cx +z =0 which is a quadratic equation. a 0. The fact that this quadratic is of second order guarantees you it has at least single solution according to the Foundational Theorem of Algebra. Solutions could be straightforward or difficult. A quadratic equation is one that has four variables. This suggests that at least on word in it ought to be squared. One of the common formulas for solving quadratic equations is "ax2 + bx + c = 0." where the undefined variable "X" is represented by the integer values or integers a, b, and c.
Here,
Given : √gF+H = u
On squaring both side :
=>gF + H = u²
=> gF= u²− H by g
.=>gF/g =u²/ g + (−H)/g
Simplify the left side.
=>F=u²/g + (−H)/g
=>F = u²/g −H/g
Therefore , the solution of the given problem of quadratic equation comes out to be F = u²/g −H/g.
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The profits in a business are to be shared by the three partners in the ratio of 3 to 2 to 5. The profit for the year was $176,500. Determine the number of dollars each partner is to receive.
For the year in which they earned $176,500, the partners will receive $52,950, $35,300, and $88,250 respectively.
Here let the partners be A, B, and C.
According to the question, A: B: C = 3: 2: 5
This implies that if the profits are divided into
3 + 2 + 5 = 10 equal parts, 3 of those parts will go to A, 2 of those parts will go to B and 5 of those parts will go to C.
Here the profits for the year are $176,500.
Now dividing them into 10 equal parts will give us the value of each part to be
$176, 500/10 = $17,650
Hence A will receive $17,650 X 3 = $52,950
B will receive $17,650 X 2 = $35,300
C will receive $17,650 X 5 = $88,250
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given ABCD,EBGF, and HJKD are parallelograms.
Answer:
see explanation
Step-by-step explanation:
• the opposite angles of a parallelogram are congruent.
Then
∠ 2 = ∠ 1
and
∠ 4 = ∠ 1
and
∠ 3 = ∠ 4
since ∠ 3 = ∠ 4 and ∠ 4 = ∠ 1 with ∠ 2 = ∠ 1 = ∠ 4
then
∠ 2 ≅ ∠ 3
By using the property of opposite angles of a parallelogram, we can say that ∠2 = ∠3.
A parallelogram is a special type of quadrilateral whose opposite sides are equal and parallel to each other. Another notable property of a parallelogram is that opposite angles are equal and sum of adjacent angles is 180 degrees.
Using the property that opposite angles of a parallelogram are equal,
In the parallelogram BEFG, ∠2 = ∠1 - equation 1
In the parallelogram DHJK, ∠4 = ∠3 - equation 2
In the parallelogram ABCD, ∠4 = ∠1 - equation 3
Equating equations 1, 2 and 3,
∠2 = ∠1 = ∠4 = ∠3
Thus implying, ∠2 = ∠3.
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whats the answer to 3 1/6 + 2 3/8?
Answer:5 13/24
Step-by-step explanation:
The correct answers is 5.54166667
→ 3 1/6 dividing
→ + 2 3/8 dividing and adding.
→ = 5.54166667
: Find the exact value of the given expression. cos(2 tan^-1 (4/3))
Exact value of the expression cos (2 [tex]tan^-^1 (\frac{4}{3})[/tex]) = -7/25 . which is the cosine of the value of an angle 2 [tex]tan^-^1 (\frac{4}{3})[/tex]) .
let [tex]tan^-^1 (\frac{4}{3})[/tex] = θ
so tan θ = 4/3
tan θ = p/b
Trignometic angle formula
so p= 4k and b= 3k where k is a constant value.
h = [tex]\sqrt{p^2+b^2}[/tex]
=> [tex]\sqrt{16k^2+ 9k^2}[/tex]
=> 25k^2
=> 5k
where p is perpendicular , b is base and h is hypotenuse
so h= 5k
sin θ = p/h
=> 4k/5k
=> 4/5
cos θ =b/h
=> 3k/5k
=> 3/5
and cos (2 [tex]tan^-^1 (\frac{4}{3})[/tex]) = cos (2θ)
cos (2θ) = 2 [tex]cos^2[/tex] θ -1
=> 2 * [tex]\frac{3}{5} ^2[/tex] - 1
=> 18/25 -1
=> -7/25
so value of cos (2 [tex]tan^-^1 (\frac{4}{3})[/tex]) = -7/25
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A total of $12,000 is invested at an annual interest rate of 3%. Find the balance after 4 years if
the interest is compounded continuously.
$13506.11
$12526.03
$13,529.96
The balance after 4 years if the interest is compounded continuously can be calculated using the formula for continuous compounding:
A = Pe^rt
where A is the balance after the period, P is the initial principal, r is the interest rate, and t is the time in years.
In this case, the initial principal is $12,000, the interest rate is 3%, and the time is 4 years.
A = 12000 * e^(0.03*4)
A = 12000 * e^0.12
A = 12000 * 1.128037
A = $13,529.96
What is used to calculate best fit line in linear regression?
The least sum of squared errors cost function is used to determine the line of best fit. The least sum of squares error will be on the line of best fit.
What is linear regression?
When predicting a variable's value based on the value of another variable, linear regression analysis is utilized. The dependent variable is the one you want to be able to forecast. The independent variable is the one that you are utilizing to forecast the value of the other variable.
What does linear regression regression mean?
A regression is a statistical approach that links a dependent variable to one or more independent (explanatory) variables.
If there are changes in one or more of the explanatory variables, a regression model can demonstrate whether changes in the dependent variable are also related.
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After a 25% discount, the price of a T-shirt was $12. What
was the price before the discount?
Answer: $15
Step-by-step explanation: 1.25 X 12 = 15
Answer:
The price before the discount is $ 16
Step-by-step explanation:
Why is the square root of 16 is equal to?
A number's square root multiplied by another number's square root does not always equal the total of these two numbers' square roots, thus the square root of 16 is equal to 4.
What is square roots?It is possible to multiply an integer by its square root in order to obtain the original value. Square root of, end square root is the symbol for this mathematical concept. Contrary to squaring, finding a number's square root is the reverse. For instance, 3 is squared at 9, 32, and its square root at 9, which is 9, is equal to 3. It is simple to multiply by 9 since it is a perfect square.
So, there is a reverse relationship between squaring and getting the square root.
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A 2-column table with 4 rows. The first column is labeled x with entries negative 5, 1, 4, 6. The second column is labeled y with entries 9, 0, negative 7, negative 1.
What is the range of the given function?
A 2-column table with 4 rows. The first column is labeled x with entries negative 5, 1, 4, 6. The range is
{9, 0, -7, -1}.
What is the range?Generally, The range is the difference between the largest and smallest values in a set of data. In statistics, it is a measure of the spread of a dataset, giving an indication of the extent to which values in the data vary. It is calculated by subtracting the minimum value from the maximum value in the dataset.
The range of a function is the set of all possible output values (y-values) of the function.
In this case, the range of the function would be {-1, 0, 7, 9}.
This is determined by looking at the y-values in the second column of the table: {9, 0, -7, -1}.
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How to answer this because I’m so confused how to graph this so can someone help
Answer:
y = 1/3 x + 4
Step-by-step explanation:
4^2 + 3|4x - 9| when x = -2
Answer:
[tex]4^2+3|4(-2)-9|\\16+3|-17|\\16+51\\\boxed{67}[/tex]
Select the best answer. Which of the following statements about the sampling distribution of the sample mean is incorrect? (a) The standard deviation of the sampling distribution will decrease as the sample size increases. (b) The standard deviation of the sampling distribution is a measure of the variability of the sample mean among repeated samples. (c) The sample mean is an unbiased estimator of the population mean. (d) The sampling distribution shows how the sample mean will vary in repeated samples. (e) The sampling distribution shows how the sample was distributed around the sample mean.
Answer:
The answer is E) The sampling distribution shows how the sample was distributed around the sample mean.
Step-by-step explanation:
Hope this helps!
Dylan opened a credit card account with $625.00 of available credit. Now that he has made some purchases, Dylan's account only has $493.75 of available credit. What is the percentage decrease of the amount of available credit in Dylan's account?
The answer is 21%
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: Dylan opened a credit card account with $625.00 of available credit. Now that he has made some purchases, Dylan's account only has $493.75 of available credit.
Thus change in amount is 625-493.75=131.25
percentage change = 131.25/625 × 100
= 21%
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Name the convex polygon whose interior angle measures have each given sum. 900 and 2520
Answer:
A convex polygon's interior angle measure is given by the formula (n-2) * 180, where n is the number of sides of the polygon. So for a polygon with an interior angle sum of 900, we have (n-2) * 180 = 900. Solving for n, we get n = 5.
For a polygon with an interior angle sum of 2520, we have (n-2) * 180 = 2520. Solving for n, we get n = 14.
So the convex polygon with an interior angle sum of 900 is a pentagon, and the convex polygon with an interior angle sum of 2520 is a 14-gon.
Step-by-step explanation:
PLEASE HELP ASAP
The graph shows the favorite colors chosen by middle school students. Which statement is supported by the information in the graph?
Exactly 42% of the students chose green, black, or purple as their favorite color.
More than 1/10 of the students chose pink as their favorite color.
Less than 18% chose blue as their favorite color.
Fewer than 30% of the students red, yellow, or orange as the favorite color.
A statement which is supported by the information in the graph include the following: A. exactly 42% of the students chose green, black, or purple as their favorite color.
How to determine the true statement?In order to determine the true statement based on the information provided in the given bar chart, we would calculate the total number of students as follows;
Total number of students = 6 + 4 + 8 + 7 + 9 + 3 + 4 + 9
Total number of students = 50 students.
For the number of students who chose green as their favorite color, we have the following:
Green = 6/50 × 100
Green = 0.14 × 100
Green = 14%.
For the number of students who chose black as their favorite color, we have the following:
Black = 8/50 × 100
Black = 0.16 × 100
Black = 16%.
For the number of students who chose purple as their favorite color, we have the following:
Purple = 6/50 × 100
Purple = 0.12 × 100
Purple = 12%.
Total percentage = 14% + 16% + 12%
Total percentage = 42%
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What is the solution to the system of equations below?
x + 3 y = 15 and 4 x + 2 y = 30
What is the solution to the system of equations below?
x + 3 y = 15 and 4 x + 2 y = 30
(6, 3)
(7, –6)
(3, 6)
(–6, 7)
Answer:
(6,3)
Step-by-step explanation:
x+3y=15
6+3×3=15
6+9=15
15=15
again
4x+2y=30
4×6+2×3=30
24+6=30
30=30
Hence the answer is (6,3)
Answer:
C.) 4,3
Step-by-step explanation:
The given system of equations is:
x + 3y = 15
4x + 2y = 30
The first equation can be rewritten as:
y = (15 - x)/3
Substituting this expression for y into the second equation gives:
4x + 2((15 - x)/3) = 30
Solving for x, we get:
x = 4
Substituting this value of x back into the first equation gives:
y = (15 - 4)/3 = 3
Therefore, the solution to the system of equations is (4,3).
A triangle ha ide with length 8, 15, and 17. Approximate the acute angle in thi triangle to the nearet degree and lit in acending order
According to Pythagoras, the square with the longest side is equal to the total of the squares with two sides. Therefore, the triangle in question has an acute angle of 28.07 degrees.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
The Pythagorean theorem is satisfied by the triangle's dimension. As a result, the triangle has a right angle.
The acute angle will then be
x = [tex]sin^{-1}8/17[/tex]
x = 28.07 degrees.
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HELPPPPP !! The cost in dollars to produce x shovels in a factory is given by the function C(x)=17x+500. The number of shovels that can be produced in h hours is
given by the function N(h)=30h.
7. Find the rule for C(N(h)).
8. Find the cost when h=8 hours.
The cost when h=8 hours is 4290.
What is function?A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. An example of a rule is a function, which produces one output for a single input. A mathematical function is a rule that determines the value of the dependent variable based on the values of the independent variables. A table, a formula, or a graph are just a few examples of how a function might be expressed.An input is connected to an output by a function. It resembles a device with an input and an output. In addition, the output is somehow connected to the input.c(x) = 12x + 450 and N(h) = 40h
We get,
C(N(h)) = 12 *(N(h)) + 450
= 12 * 40h + 450
= 480h + 450
So,
Cost when h = 8 -> 480*8 + 450 = 4290
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How many different natural numbers can be formed using the digits 0,2,3,4,5,6 lying between 10 and 1000
Answer:
The total number of numbers = 125
what is the effective annual interest rate rate offered first and loan
The effective annual interest rate offered on a loan is C. It is the interest rate that would earn the same interest with annual compounding.
What is the effective annual interest rate ?The rate of interest that an investor can earn (or pay) in a year after taking into account compounding is known as the effective annual interest rate, to put it simply.
An essential instrument for assessing the real return on an investment or the real interest rate on a loan is the effective annual interest rate.
Essentially, the effective yearly interest rate that is provided on a loan is the rate at which the same amount of interest would be earned with annual compounding.
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Options for this question include:
A. It is the interest rate for an n-year time interval, where n may be more than one year or less than or equal to one year (a fraction).B. It refers to the cash flows from an investment over a one-year period divided by the number of times that interest is compounded during the year.C. It is the interest rate that would earn the same interest with annual compounding.D. It is the ratio of the number of the annual percentage rate to the number of compounding periods per year.