Answer:
36
Step-by-step explanation:
2x is an exterior angle
Exterior angles = the sum of the two remote (unconnected - non supplementary interior angles).
Put symbolically
<LEG = <EGF + <EFG
<EFG = 180 - 4x In this case you need to find the supplemtnt
<LEG = x + 180 - 4x
2x = 180 - 3x Add 3x to both sides
5x = 180 Divide by 5
x = 36
Find the distance from the vertices of AABC to the corresponding vertices of the other three triangles, and enter them in the table. For AJKL-
you'll need to use the distance formula da (01 – 12) + (y1 - y2) . Verify your calculations using the tools available in GeoGebra.
Answer:
See explanation
Step-by-step explanation:
The question is incomplete, as the vertices of the triangle are not given.
A general explanation is as follows;
To calculate distance between two points, we use:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Take for instance;
[tex]A = (1,4)[/tex]
[tex]B = (3,-2)[/tex]
Distance AB is:
[tex]AB = \sqrt{(1 - 3)^2 + (4 - -2)^2}[/tex]
[tex]AB = \sqrt{(- 2)^2 + (4 +2)^2}[/tex]
[tex]AB = \sqrt{(- 2)^2 + (6)^2}[/tex]
Evaluate the exponents
[tex]AB = \sqrt{4 + 36}[/tex]
[tex]AB = \sqrt{40}[/tex]
[tex]AB = 6.32[/tex]
Answer:
for edmentum
Step-by-step explanation:
Find the slope of the line that passes through the two points 2,-4 & 4,-1
Answer:
Step-by-step explanation:
I have this saved on my computer in notepad b/c this type of question get asked sooo often :/
point P1 (-4,-2) in the form (x1,y1)
point P2(3,1) in the form (x2,y2)
slope = m
m = (y2-y1) / (x2-x1)
My suggestion is copy that above and save it on your computer for questions like this
now use it
Point 1 , P1 = (2,-4) in the form (x1,y1)
Point 2 , P2 = (4,-1) in the form (x2,y2)
m = [ -1-(-4) ] / [ 4-2]
m = (-1+4) / 2
m = 3 / 2
so now we know the slope is 3/2 :)
Matthew participates in a study that is looking at how confident students at SUNY Albany are. The mean score on the scale is 50. The distribution has a standard deviation of 10 and is normally distributed. Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?
a) 93.32%
b) 6.68%
c) 0.07%
d) 43.32%
Answer:
b) 6.68%
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean score on the scale is 50. The distribution has a standard deviation of 10.
This means that [tex]\mu = 50, \sigma = 10[/tex]
Matthew scores a 65. What percentage of people could be expected to score the same as Matthew or higher on this scale?
The proportion is 1 subtracted by the p-value of Z when X = 65. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{65 - 50}{10}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a p-value of 0.9332.
1 - 0.9332 = 0.0668
0.0668*100% = 6.68%
So the correct answer is given by option b.
X^2-y^2=k need the answer
Answer:
Let's solve for k.
x2−y2=k
Step 1: Flip the equation.
k=x2−y2
Answer:
k=x2−y2
Step-by-step explanation:
Find the 11th term of the sequence
3, -6, 12, -24,...
3072
6144
-6144
-3072
Answer:
-3072
Step-by-step explanation:
HELP PLEASSSSSS I will give brainlyest!!!!!!!!!!!!!!!!!!
Answer:
1/2
Step-by-step explanation:
Convert 2/3 to 4/6
Subtract: 4/6 - 1/6
You get 3/6
Simplify: 1/2
Hope this helps!
Answer: The answer is 1/2
Please help Ladder question!!
A 6 ft ladder, resting against a wall, begins to slip down the wall. When the angle of the ladder is 45 degrees, the bottom of the ladder is moving away from the wall at 0.5 m/s. At that moment, how fast is the top of ladder moving down the wall?
Answer:
Step-by-step explanation:
This is a related rates problem from calculus using implicit differentiation. The main equation is going to be Pythagorean's Theorem and then the derivative of that. Pythagorean's Theorem is
[tex]x^2+y^2=c^2[/tex] where c is the hypotenuse and is a constant. Therefore, the derivative of this with respect to time, and using implicit differentiation is
[tex]2x\frac{dx}{dt}+2y\frac{dy}{dt}=0[/tex] and dividing everything by 2 to simplify a bit:
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex]. Upon analyzing that equation, it looks like we need values for x, y, [tex]\frac{dx}{dt}[/tex], and [tex]\frac{dy}{dt}[/tex]. And here's what we were given:
[tex]\theta=45[/tex] and [tex]\frac{dx}{dt}=.5[/tex] In the greater realm of things, that's nothing at all.
BUT we can use the right triangle and the angle we were given to find both x and y. The problem we are looking to solve is to
Find [tex]\frac{dy}{dt}[/tex] at the instant that [tex]\frac{dx}{dt}[/tex] = .5.
Solving for x and y:
[tex]tan45=\frac{x}{6}[/tex] and
6tan45 = x ( and since this is a 45-45-90 triangle, y = x):
[tex]6(\frac{\sqrt{2} }{2})=x=y[/tex] so
[tex]x=y=3\sqrt{2}[/tex] and now we can fill in our derivative. Remember the derivative was found to be
[tex]x\frac{dx}{dt}+y\frac{dy}{dt}=0[/tex] so
[tex]3\sqrt{2}(\frac{1}{2})+3\sqrt{2}\frac{dy}{dt}=0[/tex] and
[tex]\frac{3\sqrt{2} }{2}+3\sqrt{2} \frac{dy}{dt}=0[/tex] and
[tex]3\sqrt{2}\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}[/tex] and multiplying by the reciprocal of the left gives us:
[tex]\frac{dy}{dt}=-\frac{3\sqrt{2} }{2}(\frac{1}{3\sqrt{2} })[/tex] so
[tex]\frac{dy}{dt}=-\frac{1}{2}\frac{m}{s}[/tex]
Given: CD is an altitude of triangle ABC.
Prove: a^2 = b^2 +c^2 = 2bccos A
Answer:
Step-by-step explanation:
Statements Reasons
1). CD is an altitude of ΔABC 1). Given
2). ΔACD and ΔBCD are right 2). Definition of right triangles.
triangles.
3). a² = (c - x)² + h² 3). Pythagoras theorem
4). a² = c² + x² - 2cx + h² 4). Square the binomial.
5). b² = x² + h² 5). Pythagoras theorem.
6). cos(x) = [tex]\frac{x}{a}[/tex] 6). definition of cosine ratio for an angle
7). bcos(A) = x 7). Multiplication property of equality.
8). a² = c² - 2c(bcosA) + b² 8). Substitution property
9). a² = b² + c² - 2bc(cosA) 9). Commutative properties of
addition and multiplication.
The center of the circle is located (3'8), and the circle has a radius that is 5 units long. What is the general form of the equation for the circle
9514 1404 393
Answer:
x² +y² -6x -16y +48 = 0
Step-by-step explanation:
Given:
circle center: (3, 8)circle radius: 5Find:
general form equation for the circle
Solution;
The standard form equation for the circle is ...
(x -h)² +(y -k)² = r² . . . . . circle with radius r centered at (h, k)
(x -3)² +(y -8)² = 5²
Subtracting 25 and expanding this will give the general form.
x² -6x +9 +y² -16y +64 -25 = 0
x² +y² -6x -16y +48 = 0
_____
Additional comment
"General form" of an equation is usually the form f(x,y) = 0, where f(x, y) is written in "standard form," with terms in lexicographical order and decreasing degree.
Find the value of x in the kite below.
60°
O
x = [?]
Answer:
30
Step-by-step explanation:
The given is right triangle with angle measure 90-60 and 30 degrees as we can see on the image.
what tearm means per hundred
a.base b.percent c.percentage d.rate
the term per hundred means percent
hope it helps
Answer:
C. Percent
Explanation:
per hundred means 1 in 100. percent is referring to the unit that is 1 in 100 of another value
1ex. 1% of 100 (1 percent of 100)
2ex. 49% of 235 (49 percent of 235)
whitch numbre produces a rational number when multiplied by 1/3 ?
Answer:
Step-by-step explanation:
multiplication of two rational numbers produce a rational number.
I need help please and thank you.
Answer:
option a.
[tex] + - \frac{13}{5} [/tex]
Step-by-step explanation:
[tex]25x^2\: - \:169 = 0 [/tex]
[tex]25x^2 = 169[/tex]
[tex] {x}^{2} = \frac{169}{25} [/tex]
[tex]x = + - \sqrt{ \frac{169}{25} } [/tex]
[tex]x = + - \frac{13}{5} [/tex]
A professor is interested in whether or not college students have a preference (indicated by a satisfaction score) for reading a textbook that has a layout of one column or layout of two columns. In the above experiment, what is the dependent variable
Answer:
Satisfaction score
Step-by-step explanation:
The dependent variable may be described as the variable which is being measured in a research experiment. In the scenario described above, the dependent variable is the satisfaction score which is used to measure preference for a one or two column textbook. The dependent variable can also seen as the variable which we would like to predict, also called the predicted variable . The predicted variable here is the satisfaction score.
Need help on this problem
Answer:
Step-by-step explanation:
[tex]2(x-2)^2=8(7+y)\\2(x-2)^2=56+8y \Rightarrow y={1\over{8}}[2(x-2)^2-56]={1\over{4}}(x-2)^2-7\\finally\\y={1\over{4}}(x-2)^2-7\\let ~change~x~and~y\\x={1\over{4}}(y-2)^2-7\\x+7={1\over{4}}(y-2)^2\\4(x+7)=(y-2)^2\\y-2=\pm\sqrt{4(x+7)}\\\\y=2\pm\sqrt{4x+28}[/tex]
A certain financial services company uses surveys of adults age 18 and older to determine if personal financial fitness is changing over time. A recent sample of 1,000 adults showed 410 indicating that their financial security was more than fair. Suppose that just a year before, a sample of 1,200 adults showed 420 indicating that their financial security was more than fair.
Required:
a. State the hypotheses that can be used to test for a significant difference between the population proportions for the two years.
b. Conduct the hypothesis test and compute the p-value. At a 0.05 level of significance, what is your conclusion?
c. What is the 95% confidence interval estimate of the difference between the two population proportions?
d. What is your conclusion?
Answer:
b) Then z(s) is in the rejection region for H₀. We reject H₀. The p-value is smaller than α/2
c)CI 95 % = ( 0.00002 ; 0.09998)
Step-by-step explanation: In both cases, the size of the samples are big enough to make use of the approximation of normality of the difference of the proportions.
Recent Sample
Sample size n₁ = 1000
Number of events of people with financial fitness more than fair
x₁ = 410
p₁ = 410/ 1000 = 0.4 then q₁ = 1 - p₁ q₁ = 1 - 0.4 q₁ = 0.6
Sample a year ago
Sample size n₂ = 1200
Number of events of people with financial fitness more than fair
x₂ = 420
p₂ = 420/1200 p₂ = 0.35 q₂ = 1 - p₂ q₂ = 1 - 0.35 q₂ = 0.65
Test Hypothesis
Null Hypothesis H₀ p₁ = p₂
Alternative Hypothesis Hₐ p₁ ≠ p₂
CI 95 % then significance level α = 5% α = 0.05 α/2 = 0.025
To calculate p-value:
SE = √ (p₁*q₁)/n₁ + (p₂*q₂)/n₂
SE = √ 0.4*0.6/1000 + 0.65*0.35/1200
SE = √ 0.00024 + 0.000189
SE = 0.021
z(s) = ( p₁ - p₂ ) / SE
z(s) = ( 0.4 - 0.35 )/0.021
z(s) = 0.05/ 0.021
z(s) = 2.38
We find p-value from z-table to be p-value = 0.00842
Comparing
p-value with α/2 = 0.025
α/2 > p-value
Then z(s) is in the rejection region for H₀. We reject H₀
CI 95 % = ( p₁ - p₂ ) ± 2.38*SE
CI 95 % = ( 0.05 ± 2.38*0.021 )
CI 95 % = ( 0.05 ± 0.04998)
CI 95 % = ( 0.00002 ; 0.09998)
CI 95 % does not contain the 0 value affirming what the hypothesis Test already demonstrate
You work for a parts manufacturing company and are tasked with exploring the wear lifetime of a certain bearing. You gather data on oil viscosity used and load. You see the regression output given below.
Predictor Coef Stdev t-ratio P
Constant -147.973 41.972 -3.53 0.004181
viscosity 6.262 0.474 13.21 <0.0001
load 0.298 0.04 7.43 <0.0001
s = 13.507 R² = 95.73% R² (adj = 95.02%
Analysis of Variance
Source DF SS MS F
Regression 2 49131.93 24565.96 134.65
Error 12 2189.38 182.45
Total 14 51321.3
Required:
What is the correct conclusion about the regression slopes based solely on the F-test
Answer:
We reject the Null and conclude that There is significant evidence that the slope values are greater than 0.
Step-by-step explanation:
Based on the ANOVA output given :
The F critical value can be obtained thus ;
F(df regression, df error)
Using an α-value of 0.01
F(2, 12) at α = 0.01 is 6.927
The F statistic as obtained from the ANOVA table = 134.65
Since, F statistic > F critical we reject the Null and conclude that slope values are significantly > 0
Similarly,
Using the Pvalue :
The Pvalue of the slope are extremely small :
Viscosity <0.0001
Load <0.0001
At α = 0.01, 0.025
The Pvalue < α ; The null will be rejected.
For the diagram below, which equation is the correct use of the distance
formula?
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Answer:
D
Step-by-step explanation:
Any equation that does not have y2 as the first term in the second set of parentheses will be incorrect.
The correct usage is shown in equation D.
help e please i’ll give brainliest
Answer:
363,000,000
..........
The function f is defined by the following rule. f(x) = 5x+1 Complete the function table.
Answer:
[tex]-5 \to -24[/tex]
[tex]-1 \to -4[/tex]
[tex]2 \to 11[/tex]
[tex]3 \to 16[/tex]
[tex]4 \to 21[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 5x + 1[/tex]
Required
Complete the table (see attachment)
When x = -5
[tex]f(-5) = 5 * -5 + 1 = -24[/tex]
When x = -1
[tex]f(-1) = 5 * -1 + 1 = -4[/tex]
When x = 2
[tex]f(2) = 5 * 2 + 1 = 11[/tex]
When x = 3
[tex]f(3) = 5 * 3 + 1 = 16[/tex]
When x = 4
[tex]f(4) = 5 * 4 + 1 = 21[/tex]
So, the table is:
[tex]-5 \to -24[/tex]
[tex]-1 \to -4[/tex]
[tex]2 \to 11[/tex]
[tex]3 \to 16[/tex]
[tex]4 \to 21[/tex]
Solve this equation log3X + log3(x-6) = log3 7
Hello!
log₃(x) + log₃(x - 6) = log₃(7) <=>
<=> log₃(x * (x - 6)) = log₃(7) <=>
<=> log₃(x² - 6x) = log₃(7) <=>
<=> x² - 6x = 7 <=>
<=> x² - 6x - 7 = 0 <=>
<=> x² + x - 7x - 7 = 0 <=>
<=> x * (x + 1) - 7 * (x + 1) = 0 <=>
<=> (x + 1) * (x - 7) = 0 <=>
<=> x + 1 = 0 and x - 7 = 0 <=>
<=> x = -1 and x = 7, x ∈ { 6; +∞ } <=>
<=> x = 7
Good luck! :)
What are the coordinates of vertex F" of ΔF"G"H"?
Which equation represents the line that passes through points (1, –5) and (3, –17)?
Answer:
equation : y= -6 + 1
Step-by-step explanation:
To teach computer programming to employees, many firms use on the job training. A human resources administrator wishes to review the performance of trainees on the final test of the training. The mean of the test scores is 72 with a standard deviation of 5. The distribution of test scores is approximately normal. Find the z-score for a trainee, given a score of 82.
Answer:
The z-score for the trainee is of 2.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The mean of the test scores is 72 with a standard deviation of 5.
This means that [tex]\mu = 72, \sigma = 5[/tex]
Find the z-score for a trainee, given a score of 82.
This is Z when X = 82. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{82 - 72}{5}[/tex]
[tex]Z = 2[/tex]
The z-score for the trainee is of 2.
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24. What could be the 2-digit number? List all options.
Given:
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24.
To find:
The 2-digit numbers.
Solution:
Let the two digit number be [tex]ab[/tex]. Then the 4 digit number will be [tex]55ab[/tex].
We know that the number [tex]55ab[/tex] lies in the range 5500 to 5599.
Now,
[tex]5500=229\times 24+4[/tex]
It means, [tex]5500-4=5496[/tex] is divisible by 24. So, the numbers lie in the range 5500 to 5599 and divisible by 24 are:
[tex]5496+24=5520[/tex]
[tex]5520+24=5544[/tex]
[tex]5544+24=5568[/tex]
[tex]5568+24=5592[/tex]
Therefore, the possible 2-digit numbers are 20, 44, 68, 92.
I need help with three
Answer:
A and F
Step-by-step explanation:
A and F both represent instances of division of 14/5
B represent multiplication
C represent the reciprocal of the problem, 5/14
D represent addition
calculate and find the area of the figure below 10m 8m 8m 2m 2m 2m 2m 2m
Answer:
can you be more specific?
Step-by-step explanation:
Which operation will solve the following word problem? Jaylene bought a blouse for $20.00. The next day she returned the blouse and got 90% of her money back, she was charged a restocking fee of 10%. How much money did she get back?
Division
Addition
Subtraction
Multiplication
Answer:
division is right i hope you understand
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Answer:
Multiplication
Step-by-step explanation:
The amount Jaylene got back is 90% of the amount she spent. That value is found by multiplying 90% times $20.
Jaylene got back ...
90% × $20 = $18
Help please and thanks !!
Answer:
4th option
Step-by-step explanation:
tanZ = [tex]\frac{opposite}{adjacent }[/tex] = [tex]\frac{XY}{ZY}[/tex]
Which choice is equivalent to √3 *√8*√5
A. 2√30
B. 4√30
C. 10√12
D. 24√5
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { A. \:2 \sqrt{30} }}}}}}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:EXPLANATION:}}}[/tex]
[tex] = \sqrt{3} \times \sqrt{8} \times \sqrt{5} [/tex]
[tex] = \sqrt{3 \times 2 \times 2 \times 2 \times 5} [/tex]
[tex] = \sqrt{ ({2})^{2} \times 2 \times 3 \times 5} [/tex]
[tex] = 2 \sqrt{2 \times 3\times 5} [/tex]
[tex] = 2 \sqrt{30} [/tex]
Note:[tex] \sqrt{ ({a})^{2} } = a[/tex]
[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]
Answer:
A. 2√30
Step-by-step explanation:
[tex] \small \sf \: \sqrt{3} \times \sqrt{8} \times \sqrt{5} \\ [/tex]
split √8
[tex] \small \sf \leadsto \sqrt{3 × 2 × 2 × 2 × 5} [/tex]
[tex] \small \sf \leadsto \: 2 \sqrt{2 \times 3 \times 5} [/tex]
[tex] \small \sf \leadsto \: 2 \sqrt{30} [/tex]