Answers
We have to solve "700 - 462" with the arrow method.
First, we look at 462 and identify the hundreds, tens and units:
We have 4 hundreds, 6 tens and 2 units.
Then, we can solve this substraction:
1) We substract a hundred 4 times.
2) Then, to the result of the previous step, we substract a ten 6 times.
3) To the result of the previous step we substract 2 units.
Answer: The result of 700 - 462 is 238.
Related Questions
a baby weights 7 pounds at birth. the table shows the birth weight after each month of life, up to six months
Answers
Answer:
they are adding by 7 because 6 +7=13
PLEASE HELP ME WITHIN 30 MINUTES ; - ;
Admission to a zoo costs $10 for adults and $6 for children. A group of 29 people attending the zoo paid a total of $222 in admission fees.
Part A
Write a system of equations to represent the situation. Let a represent the number of adult admissions, and let c represent the number of child admissions.
Answers
Answer:
a + c = 29
10a + 6c = 222
Step-by-step explanation:
Admission for each adult costs $10. Admission for each child costs $6.
A group of 29 people attended the zoo.
The total admission fees paid by the group was $222.
Answer:
$222=a x $10 + c x$6
Step-by-step explanation:
I don't think the question is complete though
For an experiment with four conditions with n = 7 each, find q. (4 pts) K = N = Alpha level .01: q = Alpha level .05: q =
Answers
For an experiment with four conditions with n = 7 each, q = 7.815 for alpha level .01 and q = 5.318 for alpha level .05.
To find q, we need to first calculate the total number of observations in the experiment, which is given by multiplying the number of conditions by the sample size in each condition. In this case, we have 4 conditions with n = 7 each, so:
Total number of observations = 4 x 7 = 28
Next, we need to calculate the critical values of q for the given alpha levels and degrees of freedom (df = K - 1 = 3):
For alpha level .01 and df = 3, the critical value of q is 7.815.
For alpha level .05 and df = 3, the critical value of q is 5.318.
Therefore, for an experiment with four conditions with n = 7 each, q = 7.815 for alpha level .01 and q = 5.318 for alpha level .05.
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to make a profit, a clothing store sells board shorts at 115% of the amount they paid for them. how much did the store pay for the board shorts shown?
Answers
You didnt give a picture of the question showing the shorts
Answer: $24.34
Step-by-step explanation:
28/X=115/100
Part/Whole= %/100
28=1.15*x
x=28/1.15
x=24.34
Theophylline is a pharmaceutical drug that is sometimes used to help with lung function. You observe a case where the lab results indicate that a sample of theophylline (initial concentration of 2.0 x 10-3 M) has been metabolized to a concentration of 1.0 x 10-3 M in 24 hours. In another 24 hours the drug concentration was 5.0 x 10-4 M. What is the rate of decomposition four (4) hours after the initial sample was taken
Answers
The fifth partial sum represents the sum of the first 5 terms in the sequence is equal to 2210.
The fifth partial sum represents the sum of the first 5 terms in the sequence.
What is the partial sum of sequence?
The partial sum of a sequence gives the sum of the first n terms in the sequence.
Thus, the fifth partial sum represents the sum of the first 5 terms in the sequence.
The given geometric sequence :
$400, $420, $441, $463, and $486.
The fifth partial sum of the above sequence will be :
$400+ $420+ $441+$463+$486=$2210
Therefore, the fifth partial sum represents the sum of the first 5 terms in the sequence equal to 2210.
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The rate of decomposition as per half life is 0.0000545 M.
what is half life?
A quantity's half-life t(1/2) is the amount of time needed for it to decrease to half of its initial value. In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe any kind of exponential decay (or, very infrequently, nonexponential decay). The biological half-life of medications and other compounds in the human body, for instance, is a term used in the medical sciences. Half-opposite life's in exponential growth is time's doubling.Drug concentration decreases from 0.002M to 0.001M in 24 hours.
Again, Drug concentration decreases from 0.001M to 0.0005 M in subsequent 24 hours.
Therefore, t(1/2) = 24 hours
K= 0.693/t(1/2) = 0.693/24 = 0.028775 per hour.
K= 2.303/t Log (No/Nt)
Log(No/Nt) =Kt/2.303 =0.05015
No/Nt= Antilog (0.05015) = 1.1224
Nt= No/1.1224 = (0.0017818 M
Rate of decomposition as per half life is calculated as
(No-Nt)/t = 0.0000545 M
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(a) Use of matrices is not allowed to solve the following problems.
(i) Prove that the vectors u = (1, −1, 0), v = (0, 1, −2), w = (2, 3, 4) are linearly independent.
(ii) Prove that the vectors u = (1, −1, 0), v = (0, 1, −2), w = (2, 1, −6) are linearly dependent.
(b) Let u and v be two vectors in R3 such that ‖u‖ = 7 and ‖v‖ = 4, find the maximum and minimum
possible values of u · v.
Answers
We prove linear dependent and linear independent vectors as follows:
(a) (i) To prove that the vectors u, v, and w are linearly independent, we need to show that the only solution to the equation au + bv + c*w = 0 is a = b = c = 0. Here, a, b, and c are scalars.
Let's assume that there exist some non-zero values of a, b, and c that satisfy the equation au + bv + c*w = 0. Then we have:
au + bv + cw = a(1,-1,0) + b*(0,1,-2) + c*(2,3,4) = (a + 2c, -a + b + 3c, -2b + 4c) = (0,0,0)
This gives us a system of three linear equations:
a + 2c = 0
-a + b + 3c = 0
-2b + 4c = 0
We can solve this system by using row operations:
The resulting row-echelon form is:
1 0 0 | -4
0 1 0 | 2
0 0 1 | -1
Since the system has a unique solution a = -4, b = 2, and c = -1, we can conclude that the vectors u, v, and w are linearly independent.
(ii) To prove that the vectors u, v, and w are linearly dependent, we need to show that there exist some non-zero values of a, b, and c that satisfy the equation au + bv + c*w = 0.
Let's assume that such values exist. Then we have:
au + bv + cw = a(1,-1,0) + b*(0,1,-2) + c*(2,1,-6) = (a + 2c, -a + b + c, -2b - 6c) = (0,0,0)
This gives us a system of three linear equations:
a + 2c = 0
-a + b + c = 0
-2b - 6c = 0
We can solve this system by using row operations:
The resulting row-echelon form is:
1 0 -2 | 0
0 1 2 | 0
0 0 0 | 0
Since the system has infinitely many solutions (e.g., a = 2t, b = -2t, and c = t for any non-zero scalar t), we can conclude that the vectors u, v, and w are linearly dependent.
(b) The dot product of two vectors u and v is given by u · v = ‖u‖ ‖v‖ cosθ, where θ is the angle between the two vectors. Since ‖u‖ and ‖v‖ are given, the maximum and minimum values of u · v will depend on the angle θ.
The maximum value of cosθ is 1, which occurs when θ = 0°. Therefore, the maximum value of u · v
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helen rolls a dice and flips a coin.
calculate the probability
Answers
Answer:
1/12
Step-by-step explanation:
dice rolling=1/6
coin flipping=1/2
Hence probability=1/6×1/2
Answer:
Dice roll = 1/6
Coin flip = 1/2
a spring has a spring constant of 283 n/m. how far is the spring compressed to the right if 129 n of force are used
Answers
The spring is compressed to 95.5 cm to the right if 129 N of force are used.
In this question, we have been given the spring constant k = 283 N/m
if 129 N of force are used then we need to find distance that the spring compressed to the right.
Let the spring stretch from the equilibrium position x.
An equation for the spring's potential energy is,
PE = 1/2 kx^2
129 = 1/2 * 283 * x^2
2 * 129 = 283 * x^2
258/283 = x^2
x^2 = 0.9117
x = 0.9548 m
x = 95.5 cm
Therefore, the spring is compressed to 95.5 cm to the right if 129 N of force are used.
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10. (1 point) Suppose after the shock, the economy temporarily stays at the short-run equilibrium, then the output gap Y
2
−Y
1
is 0.
A>
B<
C=
D incomparable with 11. ( 1 point) The inflation gap π
2
−π
1
is 0.
A>
B<
C=
D incomparable with
12. (1 point) Suppose there is no government intervention, the economy will adjust itself from short-run equilibrium to long-run equilibrium, at such long long-run equilibrium, output gap Y
3
−Y
1
0.
A>
B<
C=
D incomparable with 13. (1 point) The inflation gap π
3
−π
1
is 0.
A>
B<
C=
D incomparable with
14. (1 point) Suppose the Fed takes price stability as their primary mandates, then which of the following should be done to address the shock. A monetary easing B monetary tightening C raise the
r
ˉ
D lower the
r
ˉ
15. (1 point) After the Fed achieve its goal, the output gap Y
3
−Y
1
is 0. A > B< C= D incomparable with
Answers
Suppose after the shock, the economy temporarily stays at the short-run equilibrium, then the output gap Y2−Y1 is: B< (less than)As the output gap measures the difference between the actual output (Y2) and potential output (Y1), when the output gap is less than zero, that is, the actual output is below potential output.
The inflation gap π2−π1 is 0. C= (equal)When the inflation gap is zero, it means that the current inflation rate is equal to the expected inflation rate.12. Suppose there is no government intervention, the economy will adjust itself from short-run equilibrium to long-run equilibrium, at such long-run equilibrium, output gap Y3−Y1 is 0. C= (equal). As the long run equilibrium represents the potential output of the economy, when the actual output is equal to the potential output, the output gap is zero.13.
The inflation gap π3−π1 is 0. C= (equal) Again, when the inflation gap is zero, it means that the current inflation rate is equal to the expected inflation rate.14. (1 point) Suppose the Fed takes price stability as their primary mandates, then which of the following should be done to address the shock. B monetary tightening When the central bank takes price stability as its primary mandate, it aims to keep the inflation rate low and stable. In the case of a positive shock, which can lead to higher inflation rates, the central bank may implement a monetary tightening policy to control the inflation.
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Really Need help with this one. Nobody is answering.. please help.
The percentage of hardwood concentration in raw pulp (4%, 8%, 10%, 12%), the vat pressure (500, 750 psi), and the cooking time of the pulp (2, 4 hours) are being investigated for their effects on the mean tensile strength (kN/m) of paper. Four levels of hardwood concentration, two levels of pressure, and two cooking times are selected. The data from the experiment (in the order collected) are shown in the following table.
Hardwood (%) Pressure (psi) Cook Time (hours) Strength
12 500 2 6.91
12 500 4 8.67
12 500 2 6.52
4 750 2 6.87
12 750 4 6.99
12 500 4 8.01
12 750 2 7.97
4 500 2 5.82
10 500 4 7.96
8 750 4 7.31
8 750 2 7.05
10 500 4 7.84
8 500 2 6.06
4 750 4 6.95
10 750 2 7.40
8 750 2 6.94
4 500 4 7.20
8 500 2 6.23
10 500 2 5.99
4 750 4 6.87
8 750 4 6.80
10 750 2 7.31
12 750 2 7.81
10 750 4 7.41
4 500 2 6.04
4 750 2 6.71
8 500 4 7.82
8 500 4 7.45
4 500 4 7.30
12 750 4 7.21
10 750 4 7.45
10 500 2 6.53
(a) Perform an ANOVA to determine if hardwood concentration, pressure, and/or cooking time affect the mean tensile strength of paper. Use α=0.05.
(b) Prepare appropriate residual plots for your ANOVA analysis and comment on the model’s adequacy.
(c) Which levels of hardwood concentration, pressure, and cooking time should you use to maximize mean tensile strength.
(d) Find an appropriate regression model for this data.
(e) Prepare appropriate residual plots for your regression analysis and comment on the model’s adequacy.
(f) Using the regression equation you found in part c, predict the tensile strength for a hardwood concentration of 9%, a pressure of 650 psi, and a cooking time of 3 hours.
(g) Find a 95% prediction interval for the tensile strength for a hardwood concentration of 9%, a pressure of 650 psi, and a cooking time of 3 hours.
Answers
The ANOVA analysis shows that hardwood concentration, pressure, and cooking time significantly affect the mean tensile strength of paper. Residual plots indicate the adequacy of the model. The levels of hardwood concentration, pressure, and cooking time that maximize tensile strength should be identified
(a) The ANOVA results indicate that hardwood concentration, pressure, and cooking time significantly affect the mean tensile strength of paper at a significance level of α=0.05.
(b) Residual plots can be used to assess the adequacy of the ANOVA model. These plots can help identify any patterns or trends in the residuals. For this analysis, you can create scatter plots of the residuals against the predicted values, as well as against the independent variables (hardwood concentration, pressure, and cooking time).
If the residuals appear randomly scattered around zero without any clear patterns, it suggests that the model adequately captures the relationship between the variables.
(c) To determine the levels of hardwood concentration, pressure, and cooking time that maximize the mean tensile strength, you can calculate the average tensile strength for each combination of the independent variables. Identify the combination with the highest mean tensile strength.
(d) An appropriate regression model for this data would involve using hardwood concentration, pressure, and cooking time as independent variables and tensile strength as the dependent variable. You can use multiple linear regression to estimate the relationship between these variables.
(e) Similar to the ANOVA analysis, you can create residual plots for the regression model. Plot the residuals against the predicted values and the independent variables to assess the adequacy of the model. Again, if the residuals are randomly scattered around zero, it suggests that the model fits the data well.
(f) Using the regression equation found in part (d), you can predict the tensile strength for a hardwood concentration of 9%, a pressure of 650 psi, and a cooking time of 3 hours by plugging these values into the equation.
(g) To find a 95% prediction interval for the tensile strength, you can calculate the lower and upper bounds of the interval using the regression equation and the given values of hardwood concentration, pressure, and cooking time. This interval provides a range within which the actual tensile strength is likely to fall with 95% confidence.
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I need help on the question shown on the picture please and I'm giving brainly
Answers
Answer:
10 times larger I think
literally anybody help me please!! all you have to do is find the slope on the graph. PLEASE HELP ME ASAP!!
Answers
Answer:
m = 3
Step-by-step explanation:
rise over run
Answer:
Hope it helps you ...........
here are the score that Jenna has received on her seven quizzes 16 13 20 16 12 17 18 what is the mean
Answers
Answer:
so you're adding up all the numbers together so 16+13+20+16+12+17+18=112
then you are dividing it by how many numbers there are so there are 7 numbers in total 112÷7=16
find the area of the surface. the part of the surface z = 5 5x 3y2 that lies above the triangle with vertices (0, 0), (0, 1), (2, 1).
Answers
To find the area of the surface z = 5 + 5x + 3y^2 above the triangle with vertices (0, 0), (0, 1), and (2, 1), we need to use the surface integral formula.
First, calculate the partial derivatives with respect to x and y:
∂z/∂x = 5
∂z/∂y = 6y
Now, compute the magnitudes of the cross product of the gradient vectors:
|∂z/∂x × ∂z/∂y| = √((5^2) + (6y)^2) = √(25 + 36y^2)
The area of the surface can be found using the double integral of the magnitudes over the triangle:
Area = ∬(√(25 + 36y^2)) dA
We'll use the triangle's vertices to set the integration limits for x and y:
x: 0 to 2 - y
y: 0 to 1
Area = ∫(y=0 to 1) ∫(x=0 to 2-y) (√(25 + 36y^2)) dx dy
Evaluating this integral will provide the area of the surface above the given triangle.
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In a hypothesis test for population proportion, you calculated the p-value is 0.01 for the test statistic, which is a correct statement of the p-value?
Group of answer choices
a)The p-value indicates that it is very rare to observe a test statistics equally or more extreme when the null hypothesis is true.
b)The p-value indicates that it is very likely to observe a test statistics equally or more extreme when the null hypothesis is true.
c)The p-value is calculated assuming the alternative is true.
Answers
The p-value is 0.01, which means that it is very rare to observe a test statistic that is equal to or more extreme than the one that was actually observed. SO the option a is correct.
In the given question, in a hypothesis test for population proportion, we calculated the p-value is 0.01 for the test statistic, we have to find which statement of the p-value is correct.
The p-value is the probability of obtaining results as extreme as, or more extreme than, the observed results of a statistical hypothesis test, assuming that the null hypothesis is true. A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.
If the null hypothesis is correct, the p-value is the likelihood that a test statistic will be equal to or more extreme than the one that was actually observed. Given that the null hypothesis is correct in this situation, the p-value of 0.01 indicates that it is extremely unusual to see a test statistic as dramatic as the one that was actually seen. This shows that the alternative hypothesis is more likely to be correct and that the null hypothesis is probably not true.
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strengths and limitations of visually interpreting histograms
Answers
Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.
Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.
Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.
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which set of values could be the side lengths of a 30-60-90 triangle
Answers
Answer:
D. 6, 6\(\sqrt{3}\), 12
Step-by-step explanation:
the Pythagorean Theorem states that \(a^{2} +b^{2} =c^{2}\)
so,
\(6^{2} =36\\(6\sqrt{3}) ^{2} =108\\12^{2} =144\\36+108=144\)
Javier's Deli packs lunches for a school field trip by randomly selecting sandwiches, sides, and drinks options. Each lunch includes a sandwich (PB&J, turkey or ham and cheese), a side (cheese stick or chips), and a drink (water or apple juice). What is the probability that a student gets a lunch that includes chips and apple juice?
Answers
The probability that a student gets a lunch that includes chips and apple juice from Javier's Deli is 1/12, or approximately 0.0833.
To calculate the probability, we need to determine the number of favorable outcomes (lunches with chips and apple juice) and the total number of possible outcomes (all lunch combinations).
For the sandwich options, there are 3 choices: PB&J, turkey, and ham and cheese.
For the side options, there are 2 choices: cheese stick or chips.
For the drink options, there are also 2 choices: water or apple juice.
To find the probability of getting chips and apple juice, we multiply the probabilities of each component together. The probability of getting chips is 1/2, and the probability of getting apple juice is 1/2. Therefore, the probability of getting both chips and apple juice is (1/2) * (1/2) = 1/4.
Since there are 3 sandwich options, the probability of getting any sandwich is 1/3. Multiplying this by the probability of getting chips and apple juice, we get (1/3) * (1/4) = 1/12.
Thus, the probability that a student gets a lunch with chips and apple juice is 1/12, or approximately 0.0833.
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In ΔOPQ, q = 6.5 inches, o = 8.6 inches and ∠P=55°. Find ∠Q, to the nearest 10th of an degree.
Answers
Answer:
∠Q = 35.5°
Step-by-step explanation:
We are given;
q = 6.5 inches
o = 8.6 inches
∠P = 55°
Let's first use cosine rule to find p.
p² = q² + o² - 2qo cos P
Plugging in the relevant values;
p² = 6.5² + 8.6² - (2 × 6.5 × 8.6 × cos 55)
p² = 42.25 + 73.96 - 32.0629
p² = 84.1471
p = √84.1471
p = 9.17 inches
Using sine rule, we can find ∠Q;
p/sin P = q/sin Q
sin Q = (q•sinP)/p
sin Q = (6.5 × sin 55)/9.17
sin Q = 0.5806
Q = sin^(-1) 0.5806
Q ≈ 35.5°
Answer:
47.5
Step-by-step explanation:
From delta math
The sum of the digits of a two-digit number is seventeen. The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. What is the original number?
Answers
Therefore, the original number is 10x + y = 10(10) + 7 = 107.
Given that the sum of the digits is seventeen, we have the equation:
x + y = 17 (equation 1)
The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. The number with the digits reversed would be 10y + x.
According to the given information, we have the equation:
10y + x = 5x + 30 (equation 2)
To solve the system of equations, we can substitute equation 1 into equation 2:
10(17 - x) + x = 5x + 30
Expanding and simplifying:
170 - 10x + x = 5x + 30
170 - 30 = 5x + 10x - x
140 = 14x
x = 10
Substituting the value of x back into equation 1:
10 + y = 17
y = 7
Therefore, the original number is 10x + y = 10(10) + 7 = 107.
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Find the amount necessary to fund the given withdrawals.
Semiannual withdrawals of 270$ for 6 years, interest rate is 6.2% compounded semiannually
Answers
Answer:
the amount that necessary to fund is $2,671.61
Step-by-step explanation:
The computation of the amount is shown below;
Given that
PMT = $270
NPER = 6 × 2 = 12
RATE = 6.2% ÷ 2 = 3.1%
FV = $0
The formula is shown below:
=-PV(RATE;NPER;PMT;FV;TYPE)
After applying the above formula the present value is $2,671.61
hence, the amount that necessary to fund is $2,671.61
Write 5.54 million in ordinary form
Answers
Answer:
5,540,000Step-by-step explanation:
Write 5.54 million in ordinary form
5.54 * \(10^{6}\) =
5540000
or
5.54 * 1000000 =
5540000
The width of a 2-by-4 piece of wood is actually 3 1/2 inches. Find the total width of 30 2-by-4s laid side by side. Simplify your answer.
Answers
This is equivalent to 8.75 feet
====================================================
Explanation:
3 & 1/2 inches = 3.5 inches since 1/2 = 0.5
30 boards of this width total to 30*3.5 = 105 inches
This is equivalent to 105/12 = 8.75 feet. I'll leave the answer in inches since the original unit is inches. I would ask your teacher for further clarification.
HELP WILL MARK BRAINIEST
Answers
Answer:
Graph B
Step-by-step explanation:
I need help on this question as soon as possible
Answers
Answer:
2.5, 5, 7, 8
Step-by-step explanation:
percentage of 67 of 98
Answers
The percentages of 67 of 98 is 68.36%
Percentages and fractionsFractions are written as a ratio of two integers. According to the question we are to determine the percentage of 67 that is 98.
Fraction of 67 of 98 = 67/98
Percentage = 67/98 * 100
Percentages = 6700/98
Percentages = 68.37%
Hence the percentages of 67 of 98 is 68.36%
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the equation of the line that has a slope of
-23 that passes through the point (5, 1). Which form did you choose to write the equation in and why?
Answers
1 = -23(5) + b
1 = -115 + b, b = 116
Y = -23x + 116
I choose the slope intercept form since it was easy to calculate. The slope was given, you just need to plot in the points to find the y- intercept.
Answer:
I used the y=Mx+b equation because it has a good job showing each of the elements in the equation.
Step-by-step explanation:
The slope is -2/3 so if you add it to (5,1) it would be (3,4) as you just add three and subtract to to the point. I’m going to use for this equation as it is more simple and it gives a good job showing what each element is in the equation. M is the slope, so now we have y= -2/3x +b. To find b, substitute x and y for a point on this line which I will use the point (3,4) for. Now, multiply -2/3 by 3 and you will get -2 after. Now you have 4=-2+b which the answer would be 6.
This is just an example of finding the equation, which form I used, and why.
4a - 7 = 5
What is the answer 2 step equation
Answers
Answer:
A= 3
Step-by-step explanation:
4a - 7 = 5
move the constant to the right
4a= 5+7
divide
4a=12
Awnser:
A= 3
A 95% confidence interval of a population proportion has the limits of (64.5%,75.3%). What is the margin of error
Answers
Hence, the margin of error for this 95% confidence interval of a population proportion is 5.4%.
The margin of error for a confidence interval is the distance between the sample statistic (in this case, the sample proportion) and the confidence interval limits. To find the margin of error, we can use the formula:
Margin of error = (upper limit - lower limit) / 2
In this case, the lower limit of the 95% confidence interval is 64.5% and the upper limit is 75.3%. So the margin of error is:
Margin of error = (75.3% - 64.5%) / 2
Margin of error = 10.8% / 2
Margin of error = 5.4%
Therefore, the margin of error for this 95% confidence interval of a population proportion is 5.4%.
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I need help to find the measures and equation pls.
Answers
Answer:
Equation: 7x + 8x = 180
x = 12
∠CBA = 84
∠CFH = 96
Step-by-step explanation:
We can see that ∠CBA = ∠CFE and ∠CBD = ∠CFH.
We know that the sums of two angles on a straight line are going to be equal to 180.
∠CBA = 7x
∠CFH = 8x
To find the value of x, we must do the following:
7x + 8x = 180
15x = 180
15x/15 = 180/15
x = 12
Now we just substitute to find the angle measures:
∠CBA = 7 · 12 = 84
∠ CFH = 8 · 12 = 96