Step-by-step explanation:
I think angle A = 21 degree
because in the question there is angle A Is twice means angle a + angle a= 4G degree
2 angle a=42 degree
42 divides by 2
answer is 21 degree
Does the order in which the two transformations in a composite transformation affect the final
answer? provide an example to illustrate your answer.
The order in which the two transformations in a composite transformation affect the final answer
How to determine the composite transformation?To determine if order matters or not, I will use the following example and illustration.
Let the coordinate of point A be:
A = (2, 5)
Perform the following transformations:
Translate by (x, y + 1)Dilate by a scale factor of 2First order: Translation before dilation
The translation by (x, y + 1) would give:
A' = (2, 5 + 1)
A' = (2,6)
The dilation by a scale factor of 2 would give
A" = 2 * (2,6)
A" = (4,12)
Second order: Dilation before translation
The dilation by a scale factor of 2 would give
A' = 2 * (2,5)
A' = (4,10)
The translation by (x, y + 1) would give:
A'' = (4, 10 + 1)
A'' = (4,11)
See that the final coordinates in both orders are not the same.
Hence, the order in which the two transformations in a composite transformation affect the final answer
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Find CE. pleaseee help
Answer:
Radius = 20+5 = 25
We can find CE with the pythagorean theorem
20^2 + CE^2 = 25^2
CE = 15
factorize x^4 + 2x^3 - 11x^2 - 12x + 36
I need the steps.
Please i need this for today.
[tex]x^4 +2x^3 -11x^2-12x+36\\ \\=x^4-2x^3+4x^3-8x^2-3x^2 +6x-18x+36\\\\=x^3(x-2) +4x^2(x-2) -3x(x-2) -18(x-2)\\\\=(x-2)(x^3 +4x^2 -3x -18)\\\\=(x-2)(x^3+3x^2+x^2+3x-6x-18)\\\\=(x-2)\textbf{[}x^2(x+3)+x(x+3)-6(x+3)\textbf{]}\\\\=(x-2)(x+3)(x^2 +x -6)\\\\=(x-2)(x+3)(x^2 +3x -2x-6)\\\\=(x-2)(x+3)\textbf{[}x(x+3) -2(x+3)\textbf{]}\\\\=(x-2)(x-2)(x+3)(x+3)\\\\=(x-2)^2(x+3)^2[/tex]
The ruins of a pyramid has 49 blocks in the bottom row. Each additional row has two less blocks than the first. If there are 15 rows in total:
There are 18 blocks in the first row
The missing part of the questionCalculate the number of blocks on the first row
How to determine the number of blocks?The ruin is given as:
Ruin = 49
The common difference is given as:
d = -2
The number of block on each row is then represented as:
Blocks = 48 - 2n
Where n represents the number of rows.
In this case, the first row would have a value of n = 15
So, we have:
Blocks = 48 - 2 * 15
Evaluate
Blocks = 18
Hence, there are 18 blocks in the first row
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1. Find the area of the shaded area of this figure:
PYTHAGOREAN THEOREM IN 3D URGENT PLEASE PHOTO INSERTED
To find the length of the diagonal, we need to calculate the length of the base first and then use the value to calculate the diagonal since we are given the value of height of the triangle.
Pythagorean TheoremThis theorem is used to find the missing side of a right angle triangle given that we have the length of two sides.
To calculate the base of the triangle, let's use Pythagorean theorem here
[tex]x^2 = y^2 + z^2\\x^2 = 2^2 + 3^2\\x^2 = 4 + 9 \\x^2 = 13\\x = \sqrt{13} \\x = 3.61[/tex]
Having the length of the base, let's consider the height of the triangle which is 6 and substitute the values.
[tex]d^2 = 6^2 + 3.61^2\\d^2 = 36 + 13.0321\\d^2 = 49.0321\\d = \sqrt{49.0321} \\d = 7.00[/tex]
From the calculations above, the values of the triangle are
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Hypothesis Test for the Population Mean (II)
A team averaging 110 points is likely to do very well during the regular season. The coach of your team has hypothesized that your team scored at an average of less than 110 points in the years 2013-2015. Test this claim at a 1% level of significance. For this test, assume that the population standard deviation for relative skill level is unknown.
You are to write this code block yourself.
Use Step 3 to help you write this code block. Here is some information that will help you write this code block. Reach out to your instructor if you need help.
The dataframe for your team is called your_team_df.
The variable 'pts' represents the points scored by your team.
Calculate and print the mean points scored by your team during the years you picked.
Identify the mean score under the null hypothesis. You only have to identify this value and do not have to print it. (Hint: this is given in the problem statement)
Assuming that the population standard deviation is unknown, use Python methods to carry out the hypothesis test.
Calculate and print the test statistic rounded to two decimal places.
Calculate and print the P-value rounded to four decimal places.
The test statistic is -0.46 and the p-value is gotten as 0.3340
How to Calculate the P-value?The question is not complete because the data from the sample is 105, 107, 117, 106, 110.
Mean of sample is;
Mean = (105 + 107 + 117 + 106 + 110)/5
Mean; x' = 109
From online standard deviation calculator, the standard deviation of the sample is; S = 4.848
Now, the claim is that your team scored an average significantly less than 110 points. Thus, let's define the hypothesis as;
Null Hypothesis; μ = 110
Alternative Hypothesis; μ < 110
standard error of the mean; S_m = S/√n
S_m = 4.848/5
S_m = 2.17
Thus, the t-statistic is;
t = (x' - μ)/S_m
t = (109 - 110)/2.17
t = -0.46
Degree of freedom for this sample size is;
D.F = N - 1 =5 - 1 = 4
From online p-value from t-score calculator, we have;
p-value = 0.3340
The p-value is greater than the significance value and as such we fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that your team scored an average significantly less than 110 points.
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there is 1 litre of tea in a teapot, alex pours 275ml of the tea into a cup what percentage of the tea has alex poured
Answer:
27.5%
Step-by-step explanation:
Given:
1 Liter In TeapotAlex poured 275 milliliters of the tea into a cupReview:
1,000 Milliliters = 1 LiterConcepts:
A liter is a noun meaning a unit of capacity redefined in 1964 by a reduction of 28 parts in a million to be exactly equal to one cubic decimeter. It is equivalent to 1.0567 U.S. liquid quarts and is equal to the volume of 1 kilogram of distilled water at 4°C.A millimeter is a noun meaning a unit of capacity equal to one thousandth of a liter, and equivalent to 0.033815 fluid ounce, or 0.061025 cubic inch.Formula:
The mℓ to ℓ formula is [L] = [mL] / 1000.Now we must convert 275 milliliters to liters.
1. Divide the volume by 1,000.
275 ÷ 1000 = 0.275
2. Add the Unit Symbol for Liter.
0.275 ⇒ 0.275 L
Now we have to find how much of 1 liter- 0.275 liters as a percentage is.
To convert 0.275 to percent multiply 0.275 by 100. The result is 27.5 percent, or, using the percent sign, 27.5 %.
Suppose that a, b, x and y are real numbers such that ax+by = 1, ax² + by² = 11, ax³ + by³ = 25 and ax⁴ + by⁴ = 83. Find the value of ax⁵ + by⁵.
Answer:
[tex]ax^5+ by^5=241[/tex]
Step-by-step explanation:
Given:
[tex]ax + by = 1[/tex][tex]ax^2+ by^2 = 11[/tex][tex]ax^3+ by^3 = 25[/tex][tex]ax^4+ by^4 = 83[/tex]We can re-write the left sides of the given equations as follows:
[tex]ax^2+ by^2=(ax+by)(x+y)-xy(a+b)[/tex]
[tex]ax^3+ by^3=(ax^2+by^2)(x+y)-xy(ax+by)[/tex]
[tex]ax^4+ by^4=(ax^3+by^3)(x+y)-xy(ax^2+by^2)[/tex]
Therefore, following this pattern:
[tex]ax^5+ by^5=(ax^4+by^4)(x+y)-xy(ax^3+by^3)[/tex]
Use the given values and the expanded expressions to create 2 equations to help find the values of (x+y) and xy:
Equation 1
[tex]ax^3+ by^3=(ax^2+by^2)(x+y)-xy(ax+by)[/tex]
[tex]\implies 25=11(x+y)-xy(1)[/tex]
[tex]\implies 25=11(x+y)-xy[/tex]
Equation 2
[tex]ax^4+ by^4=(ax^3+by^3)(x+y)-xy(ax^2+by^2)[/tex]
[tex]\implies 83=25(x+y)-xy(11)[/tex]
[tex]\implies 83=25(x+y)-11xy[/tex]
Multiply Equation 1 by 11:
[tex]\implies 275=121(x+y)-11xy[/tex]
Then subtract Equation 2 from this to eliminate 11xy and find the value of (x+y):
[tex]\implies 192=96(x+y)[/tex]
[tex]\implies (x+y)=2[/tex]
Multiply Equation 1 by 25:
[tex]\implies 625=275(x+y)-25xy[/tex]
Multiply Equation 2 by 11:
[tex]\implies 913=275(x+y)-121xy[/tex]
Subtract the 2nd from the 1st to eliminate 275(x+y) and find the value of xy:
[tex]\implies 288=-96xy[/tex]
[tex]\implies xy=-3[/tex]
Therefore, we now have:
[tex]ax^4+ by^4 = 83[/tex][tex]ax^3+ by^3 = 25[/tex][tex](x+y)=2[/tex][tex]xy=-3[/tex]Substitute these into the equation for ax⁵ + by⁵ and solve:
[tex]\implies ax^5+ by^5=(ax^4+by^4)(x+y)-xy(ax^3+by^3)[/tex]
[tex]\implies ax^5+ by^5=(83)(2)-(-3)(25)[/tex]
[tex]\implies ax^5+ by^5=166+75[/tex]
[tex]\implies ax^5+ by^5=241[/tex]
Where is the other endpoint located if the midpoint is at (0,-5) and one of the endpoints is (-3,-2)?
Answer:
3,-8
Step-by-step explanation:
x: from -3 to 0 is +3 add +3 more 3
y: from -2 to -5 is -3 add -3 more -8
Lisa kicked a ball against the wall at the indicated angle. what is the measure, in degrees, of <1?
The measure of angle ∠1 will be 68 degrees.
The missing graph is given below.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
The diagram is given below.
Then the measure of angle ∠1 will be
68° + 44° + ∠1 = 180°
∠1 = 68°
The measure of angle ∠1 will be 68 degrees.
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heyyy.... can someone pls help asap. Rearrange the formula to write r in terms of P and pi.
[tex]p = 2r + \pi \: r[/tex]
Step-by-step explanation:
p = 2r + pi×r
p = r(2 + pi)
r = p/(2 + pi)
Answer:
r = [tex]\frac{p}{2+\pi }[/tex]
Step-by-step explanation:
p = 2r + πr ← factor out r from each term
p = r(2 + π) ← divide both sides by (2 + π )
[tex]\frac{p}{2+\pi }[/tex] = r
Find the sum of the following series.
PLEASE SOMEONE HELP!!!
The given sum for n = 1 to n = 15 is equal to 255, so the correct option is B.
How to find the sum of the given series?
We want to find the sum of the series whose elements are of the form:
(2n + 1)
From n = 1 to n = 15.
Then our sum will be:
(2*1 + 1) + (2*2 + 1) + ... + (2*15 + 1).
3 + 5 + ... + 31
This is the sum of all odd numbers in the interval [3, 31]
Which gives:
[tex]S = 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 = 255[/tex]
So the correct option is B.
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Find the value that completes the proportion. 27/90 = 3/?
a. 10
b. 27
c. 9
d. 3
Answer:
a. 10.
Step-by-step explanation:
27 / 3 = 9
90/10 = 9
So it's 10.
Christian owns a small business selling bagels. He knows that in the last week 10 customers paid cash, 14 customers used a debit card, and 38 customers used a credit card. Based on these results, express the probability that the next customer will pay with a credit card as a decimal to the nearest hundredth.
The probability that the next customer will pay with a credit card is 0.61.
What is probability?Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it.
Given that Cristian's customers pay using, cash, debit cards and credit cards,
He knows that in the last week 10 customers paid cash, 14 customers used a debit card, and 38 customers used a credit card.
We need to find the probability that the next customer will pay with a credit card,
Therefore,
The favorable outcomes = 38
Total outcomes = 38+10+14 = 62
Therefore,
P(credit cards) = 38/62 = 0.61
Hence the probability that the next customer will pay with a credit card is 0.61.
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hat is the slope of the linear relationship shown in this table of values?
x y
-4 11
2 -1
5 -7
By using any two of the points in the table, we will see that the slope is -2.
How to get the slope for the linear relationship?
A general linear relationship is:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that if the line passes through (x₁, y₁) and (x₂, y₂), the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we can use the first two points on the table:
(-4, 11) and (2, -1), so the slope is:
[tex]a = \frac{11 - (-1)}{-4 - 2} = 12/-6 = -2[/tex]
Then the slope of the line is -2.
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Question meant for only the smartest. Please help would be much appreciated!
Answer:
the length of DE is 1/2*9 = 4.5
Mallory took out a loan for $1500. She paid the loan back in 1 year with 7% simple interest. How much did Mallory pay in total?
Answer:
$1605
Step-by-step explanation:
Because this is simple interest, you can convert the 7% into a decimal
Because she payed an EXTRA 7% she payed 107% total
107% is the equivalent to 1.07
By multiplying 1500 x 1.07 = 1605
For tax purposes, a car rental company assumes each car in their fleet depreciates by 6% per year. If the initial value of a car is $38,800.00, what will the value be when the car is 10 years old?
Options:
a.) $20,898.27
b.) $31,702.42
c.) $28,612.06
d.) $62,694.80
The value of a car after 10 years be $20898.27 if the car rental company assumes each car in their fleet depreciates by 6% per year option (a) $20898.27 is correct.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always a positive. It denotes with exponent [tex]\rm y = a^x[/tex]
where a is a constant and a>1
We can solve this problem by exponential function:
The word depreciate means the price is decreasing.
We can find the value be when the car is 10 years old:
p = 38800(1 - 0.06)¹⁰
p = 38800(0.94)¹⁰
p = 20898.266 ≈ $20898.27
Thus, the value of a car after 10 years be $20898.27 if the car rental company assumes each car in their fleet depreciates by 6% per year option (a) $20898.27 is correct.
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Is 1 1/7 a rational number?
Answer:
Yes, it is rational because it is a fraction. All rational numbers are either decimals or fractions. Since a fraction can also be represented as division, creating a decimal when divided, it counts as a rational number.
Solve the following quadratic equation 5x^2+18x+9=0
Answer:
[tex]x = -3~\text{and}~ x = -\dfrac 35[/tex]
Step-by-step explanation:
[tex]~~~~~~5x^2 +18x +9=0\\\\\implies 5x^2 +15x +3x +9 = 0\\\\\implies 5x(x+3) +3(x+3) = 0\\\\\implies (x+3)(5x+3) = 0\\\\\implies x = -3,~ x = -\dfrac 35[/tex]
Answer:
x = -3
OR
x = -(3/5)
Step by step explanation:
Given:
5x^2+18x+9=0To Find:
xSoln:
Use quadratic formulae:
Here I typed Quadratic formula as x[tex] \rm x=\cfrac{-b\pm\sqrt{b^2-4ac}}{2}[/tex]
According to the question,on the formula,
a = 5b = 18c = 9So substitute them on the formula:
THEN solve for x.
[tex] \rm \implies \: x = \cfrac{-1 8 \pm \sqrt{18 {}^{2} - 4(5 \times 9) }}{2 \times 5} [/tex]
[tex] \rm \implies \: x = \cfrac{-1 8 \pm \sqrt{324- 20 \times 9) }}{10} [/tex]
[tex]\rm \implies \: x = \cfrac{-1 8 \pm \sqrt{324- 180}}{10} [/tex]
[tex] \rm \implies \: x = \cfrac{ - 18 \pm \sqrt{144} }{10} [/tex]
[tex] \rm \implies \: x = \cfrac{ - 18 \pm12}{10}[/tex]
[tex] \rm \implies \: x = \cfrac{9 \pm 6}{5} [/tex]
Final solution will after adding first(9+6),then secondly subtracting both 9-6
[tex] \rm \implies \boxed{x = - \cfrac{3 }{5} }[/tex]
[tex] \implies \boxed{\rm x = - 3}[/tex]
So there'll be two possible answers.
What is the area of the figure? The figure is not drawn to scale.
A. 5.1 cm2
B. 11.7 cm2
C. 27.72 cm2
D. 55.44 cm2
Area of a Parallelogram = base x height
base = 3.3
height = 8.4
Area = 3.3 x 8.4 = 27.72
Answer: 27.72 cm^2
Hope this helps!
What is the value of log 256/ log 1024
Answer:
0.8
Step-by-step explanation:
The change of base formula for logarithms can be used to find this value exactly. (Your calculator can also tell you.)
[tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}[/tex]
__
Using this relation with the given numbers, we have ...
[tex]\dfrac{\log(256)}{\log(1024)}=\dfrac{\log(2^8)}{\log(2^{10})}=\dfrac{8\cdot\log(2)}{10\cdot\log(2)}=\dfrac{8}{10}\\\\\boxed{\dfrac{\log(256)}{\log(1024)}=0.8}[/tex]
The original price of a sweatshirt is $50. The sale price is 75% off the original price. Find the sale price of the sweatshirt.
Answer:
$87.5
Step-by-step explanation:
Original price also means COST PRICE
C.P=$50
S.P=75% of $50-$50
To find the sale price it will be 75% of C.P -C.P
75% × $50 + $50= 0.75 × $50-$50
=$37.5-$50.
= $12.5
therefore the sale price is $12.5
THANK YOU
The price of the sweatshirt at the sale is $12.5 which is 75% off of the original price.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, The original price of a sweatshirt is $50.
Also given that the sale price is 75% off the original price So, the cost of the sweatshirt is (100 - 75)% = 25% of the original price which is,
= (25/100)×50.
= $12.5.
So, The sale price of the sweatshirt is $12.5.
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PLEASE HELP ME!!! It’s High School Math. Algebra 2 and it’s on Big Ideas Math.
Answer:
hope this will help you
[tex]let \: the \: angle \: be \: \alpha \\ \cos( \alpha ) = \frac{b}{h} \\ \cos(60) = \frac{x}{9} \\ \frac{1}{2} = \frac{x}{9} \\ x = \frac{9}{2} \\ x = 4.5[/tex]
It+is+said+60%+of+families+own+a+pet. +of+a+sample+of+95+families,+70+owned+pets. +perform+a+hypothesis+test+to+determine+whether+the+percent+of+families+who+own+pets+is+different+than+60%
There is sufficient evidence to conclude that, the percentage of the families who own a pet is different than 60%.
What are null hypotheses and alternative hypotheses?In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
It Is said That 60% of families own a pet.
Of a sample of 95 families, 70 owned pets.
Whether the percent of families who own pets is different than 60%.
Let P be a proportion of the family who owns pets
Then by the test, we have
H₀: P = 0.60
Hₐ: P ≠ 60
Then by the test statistic, we have
[tex]z_o = \dfrac{\bar{P} - P_o}{\sqrt{\dfrac{P_o(1 - P_o)}{n}}}[/tex]
Where
[tex]\bar P[/tex] = sample proportion
P₀ = hypothesis proporion
n = sample size
Then we have
[tex]\bar P[/tex] = x/n
[tex]\bar P[/tex] = 70/95
[tex]\bar P[/tex] = 0.74
Then the test statistic will be
[tex]z_o = \dfrac{0.74-0.60}{\sqrt{\dfrac{0.60(1-0.60)}{95}}}[/tex]
z₀ = 2.785
Then the critical region will be
Critical value = ± [tex]z_{\alpha /2}[/tex]
α = 0.05
α/2 = 0.025
Then we have
z₀.₀₂₅ = 1.96
Then the critical value will be
Critical value = ± 1.96
We reject if [tex]|z_o| > |z_{\alpha /2}|[/tex]
We have
[tex]|z_o| > |z_{\alpha /2}|\\[/tex]
2.79 > 1.96
We reject the null hypothesis at a 5% significance level.
There is sufficient evidence to conclude that, the percentage of the families who own a pet is different than 60%.
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What is the length of the major axis of the conic section shown below? (x-3)^2/25+(y+2)^2/49=1
this is the answer hope it helps please if am wrong ask another person
thank you
Answer:
the answer is 14
Step-by-step explanation:
precalculus honors
Antra calculated the product 2222 × 2223 × 22 × 24 and got a number. What will be the remainder when the product is divided by 10?
Answer:
the remainder is 8
Step-by-step explanation:
2222 x 2223 x 22 x 24 = 2,608,059,168
2,608,059,168 ÷ 10 = 260,805,916.8
so the remainder is 8
2x + 5y = -16 solve for Y
Answer:
y = -(2x+16) / 5
Step-by-step explanation:
2x + 5y = -16
5y = -2x - 16
y = (-2x - 16) / 5
y = -(2x+16) / 5
In multiplication, what is the inverse
of this number?
Give your answer in lowest terms.
1000
450
The multiplicative inverse of 1000/450 is 9/20
How to determine the inverse of the number?The multiplicative inverse of a number x is:
Inverse = 1/x
The number is given as: 1000/450.
So, we have:
Inverse = 1/(1000/450)
Evaluate the expression
Inverse = 450/1000
Simplify
Inverse = 9/20
Hence, the multiplicative inverse of 1000/450 is 9/20
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