Answers
Answer:
acute isosceles triangle
vertex angle, y = 44.0 degrees. (smallest angle)
Step-by-step explanation:
If the sides are in the ratio 4:4:3,
two of the sides have equal lengths, so it is an isosceles triangle.
Also, the sum of square of the two shorter sides is greater than the square of the longest side, so it is an acute triangle.
To find the smallest angle, we draw the perpendicular bisector of the base (side length 3) and form two right triangles.
The base angle x is given by the ratio
cos(x) = 1.5/4 = 3/8
Consequently the base angle is arccos(3/8) = 68.0 degrees.
The vertex angle equals twice the complement of 68.0
vertex angle, y = 2 (90-68.0) = 44.0 degrees. (smallest angle)
Related Questions
What is the simplified form of 144x^36?
O 12x6
O 12x18
O 72x6
072x18
Answers
Answer:
B
Step-by-step explanation:
Factories A, B and C produce computers. Factory A produces 4 times as manycomputers as factory C, and factory B produces 7 times as many computers asfactory C. The probability that a computer produced by factory A is defective is0.04, the probability that a computer produced by factory B is defective is 0.02,and the probability that a computer produced by factory C is defective is 0.03. Acomputer is selected at random and found to be defective. What is the probabilityit came from factory A?
Answers
Answer:
The probability is [tex]P(A') = 0.485[/tex]
Step-by-step explanation:
Let assume that the number of computer produced by factory C is k = 1
So From the question we are told that
The number produced by factory A is 4k = 4
The number produced by factory B is 7k = 7
The probability of defective computers from A is [tex]P(A) = 0.04[/tex]
The probability of defective computers from B is [tex]P(B) = 0.02[/tex]
The probability of defective computers from C is [tex]P(C) = 0.03[/tex]
Now the probability of factory A producing a defective computer out of the 4 computers produced is
[tex]P(a) = 4 * P(A)[/tex]
substituting values
[tex]P(a) = 4 * 0.04[/tex]
[tex]P(a) = 0.16[/tex]
The probability of factory B producing a defective computer out of the 7 computers produced is
[tex]P(b) = 7 * P(B)[/tex]
substituting values
[tex]P(b) = 7 * 0.02[/tex]
[tex]P(b) = 0.14[/tex]
The probability of factory C producing a defective computer out of the 1 computer produced is
[tex]P(c) = 1 * P(C)[/tex]
substituting values
[tex]P(c) = 1 * 0.03[/tex]
[tex]P(b) = 0.03[/tex]
So the probability that the a computer produced from the three factory will be defective is
[tex]P(t) = P(a) + P(b) + P(c)[/tex]
substituting values
[tex]P(t) = 0.16 + 0.14 + 0.03[/tex]
[tex]P(t) = 0.33[/tex]
Now the probability that the defective computer is produced from factory A is
[tex]P(A') = \frac{P(a)}{P(t)}[/tex]
[tex]P(A') = \frac{ 0.16}{0.33}[/tex]
[tex]P(A') = 0.485[/tex]
Which of the following is 18x2/6x simplified?
3x
9x
4x
x/3
Answers
Answer:
3x
Step-by-step explanation:
18 x^2 / 6x
Divide the numbers
18/6 =3
Then divide the variables
x^2 /x = x
The result is 3x
Answer:
3x
Step-by-step explanation:
18x^2/6x
x^2 / x is x
18x/6
18/6 is 3
it all simplifies into 3x
Help thank you!!!!!!!
Answers
[tex] v = \sqrt{4900} + \sqrt{8100} = 70 + 90 = 160[/tex]
Answer: D. 160
What value of x is I the solution set of 3(x-4)>5x+2
Answers
Answer:
-7 > x
Step-by-step explanation:
3(x-4)>5x+2
Distribute
3x-12>5x+2
Subtract 3x from each side
3x-12-3x>5x-3x+2
-12 > 2x+2
Subtract 2 from each side
-12-2>2x+2-2
-14 > 2x
Divide by 2
-14/2 > 2x/2
-7 > x
Answer:
[tex]\boxed{x<-7}[/tex]
Step-by-step explanation:
3(x-4)>5x+2
Expand brackets.
3x - 12 > 5x+2
Subtract 3x and 2 on both sides.
-12 - 2 > 5x - 3x
-14 > 2x
Divide both sides by 2.
-7 > x
Switch sides.
x < -7
A newsgroup is interested in constructing a 95% confidence interval for the proportion of all Americans who are in favor of a new Green initiative. Of the 556 randomly selected Americans surveyed, 421 were in favor of the initiative. Round answers to 4 decimal places where possible.
Required:
a. With 99% confidence the proportion of all Americans who favor the new Green initiative is between ______ and______ .
b. If many groups of 593 randomly selected Americans were surveyed, then a different confidence interval would be produced from each group. About ________percent of these confidence intervals will contain the true population proportion of Americans who favor the Green initiative and about _______? percent will not contain the true population proportion.
Answers
Answer:
(A) With 99% confidence, the proportion that favours the Green initiative is between 418.895 and 423.105 (no approximation; answers were gotten exactly in 3 decimal places).
(B) If many groups of 593 (greater than the initial sample size of 556) randomly selected Americans were surveyed then a different confidence interval would be used or produced from each group.
About 90% of these confidence intervals will contain the true population proportion of Americans who favour the Green initiative and about 10% will not contain the true population proportion.
Step-by-step explanation:
(A) 99% of 421 = 416.79
421 - 416.79 = 4.21
4.21 ÷ 2 = 2.105
(421-2.105), (421+2.105)
The lower and upper limits are:
[418.895 , 423.105]
(B) A wider confidence interval such as 90% will be better suited in a case of multiple samples like this.
Find ZABD if ZABC = 121° in the given figure.
Answers
4x+21+3x-5=121
7x+16=121
x=15
angle ABD =4(15)+21=81
Identify the value of the CRITICAL VALUE(S) used in a hypothesis test of the following claim and sample data:
Claim: "The average battery life (between charges) of this model of tablet is at least 12 hours."
A random sample of 80 of these tablets is selected, and it is found that their average battery life is 11.58 hours with a standard deviation of 1.93 hours. Test the claim at the 0.05 significance level.
a. -0.218
b. -1.645
c. -1.946
d. -1.667
Answers
Answer:
C
Step-by-step explanation:
The critical value we are asked to state in this question is the value of the z statistic
Mathematically;
z-score = (x- mean)/SD/√n
From the question
x = 11.58
mean = 12
SD = 1.93
n = 80
Substituting this value, we have
z= (11.58-12)/1.93/√80 = -1.946
Applications of exponential functions need help ASAP PlZ
Answers
Answer:
Second choice is correct.
Step-by-step explanation:
Simple interest = $12600
Compounded interest = $14656
Best Regards!
A researcher measures job satisfaction among married, single, and divorced employees to determine whether marital status can influence job satisfaction. Based on the following description in APA format, state the value for k, N, and n. A one-way analysis of variance showed that job satisfaction did not vary by marital status, F(2, 24) = 1.93, p > 0.05.
a. k = _____
b. N = _____
c. n = _____
Answers
Answer:
a. k = 3
b. N = 27
c. n = 9
Step-by-step explanation:
Given that,
Source : sS dF mS F
Between: k -1 sSB/k-1 mSB
within N-K sSw/N-K mSw
total N-1
Therefore F ( 2, 24 ) = F ( K - 1, N - K )
so K - 1 = 2
K = 2 + 1
K = 3
N - K = 24
N - 3 = 24
N = 24 + 3
N = 27
married, single and divorced are equal sizes
so n = N/3
n = 27 / 3
n = 9
a. k = 3
b. N = 27
c. n = 9
Condense each expression. 5 log5 x - 1/4 log5 (8 -x)
Answers
Step-by-step explanation:
5 log₅ x − ¼ log₅ (8−x)
log₅ x⁵ − log₅ (8−x)^¼
log₅ x⁵ − log₅ ∜(8−x)
log₅ (x⁵ / ∜(8−x))
The expression 5 log₅ x - 1/4 log₅ (8 - x) can be condensed to [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , using the laws of logarithms and exponents.
What are logarithmic expressions?A logarithmic expression x = logₐb, implies that aˣ = b.
What are the properties used in solving logarithmic expressions?Some properties used to solve logarithmic expressions are:
Power law: logₐ xⁿ = n.logₐ xProduct law: logₓ a + logₓ b = logₓ abQuotient law: logₓ a - logₓ b = logₓ a/bHow to solve the given question?In the question, we are asked to condense the expression:
5 log₅ x - 1/4 log₅ (8 - x)
= [tex]log_{5}x^{5} - log_{5}(8 - x)^{1/4}[/tex], (using the power law: logₐ xⁿ = n.logₐ x)
= [tex]log_{5}x - log_{5}\sqrt[4]{8 - x}[/tex], (since, [tex]x^{1/a} = \sqrt[a]{x}[/tex])
= [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , (using the quotient law: logₓ a - logₓ b = logₓ a/b).
∴ The expression 5 log₅ x - 1/4 log₅ (8 - x) can be condensed to [tex]log_{5} \frac{x^5}{\sqrt[4]{8-x} }[/tex] , using the laws of logarithms and exponents.
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If my car averages 27 miles to the gallon, how many miles can I drive on3/4 tank of gas
Answers
Answer:
20.25 miles
Step-by-step explanation:
If your car travels 27 miles on a full tank of gas, then your car will travel [tex]27\cdot\frac{3}{4}[/tex] miles on [tex]\frac{3}{4}[/tex] tank of gas.
[tex]27 \cdot 0.75 = 20.25[/tex]
I hope this helped!
Write the equation of the function of a parabola with vertex at (–1,–2) and a point (1,–6) that lies on the curve.
Answers
Answer:
f(x) = -(x + 1)² - 2
Step-by-step explanation:
f(x) = a(x - h)² + k
-6 = a(1 - -1)² + -2
-6 = a(4) -2
-4 = 4a
a = -1
f(x) = -(x + 1)² - 2
in how many ways cvan 5 people be chosen and arranged in a straight line, if there are 6 people to choose from'
Answers
Answer:
720 different waysStep-by-step explanation:
Permutation has to do with arrangement. If r objevt selected from n pool of objects are to be arranged in a straight line, this can be done in nPr number of ways.
nPr = n!/(n-r)!
If 5 people are to be chosen and arranged in a straight line, if there are 6 people to choose from, this can be done in 6P5 numbe of ways.
6P5 = 6!/(6-5)!
6P5 = 6!/1!
6P5 = 6*5*4*3*2*1
6P5 = 720 different ways
helpppppppppppppppppppppp i will give star thanks bralienst
Answers
Answer:
90/x=70/100 that's my answer
[tex]90 \x = 70 \100[/tex]
Answer:
90/x = 70/100
Step-by-step explanation:
Is means equals and of means multiply
90 = 70% *x
Changing to decimal form
90 = .70x
Changing to fraction form
90 = 70/100 *x
Divide each side by x
90/x = 70/100
The price of a particular model car is $13,857 today and rises with time at a constant rate of $1203 per year. How much will a new car cost in 4.7 years?
Answers
Answer:
It should be about $19,500
Step-by-step explanation:
Answer:
$19,511.10
Step-by-step explanation:
1203*4.7= The total change over 4.7 years.
1203*4.7=5654.10
5654.10+13857=The total price after 4.7 years.
5654.10+13857=19,511.10
if f(x)=3x+7 what is f(2)
Answers
Answer:
13
Step-by-step explanation:
f(x) = 3x + 7
f(2) = 3(2) + 7
f(2) = 6 + 7
f(2) = 13
Which number is an integer? Negative three-fourths 0 2.3 Pi
Answers
Answer:
0
Step-by-step explanation:
An integer is colloquially defined as a number that can be written without a fractional component.
-3/4 ---- It is a fraction itself, so it is a fractional component
0 ---- Has no fractional component
2.3 Pi ---- Pi is irrational and is a decimal, so is 2.3. Most of this is a fractional component already.
The only one we can't eliminate using just the definition is 0.
Hope that helps, tell me if you need a further explanation
From the given numbers the number that is an integer is 0. The correct option is B.
What is an integer?An integer is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.
Given the following numbers -(3/4), 0, 2.3, and π. Therefore, from the given numbers the number that is an integer is 0.
Hence, From the given numbers the number that is an integer is 0.
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For a certain bathtub, the cold water faucet can fill the tub in 9 minutes. The hot water faucet can fill the tub in 11 minutes. If both faucets
are used together, how long will it take to fill the tub?
Do not do any rounding.
Answers
Answer:
2 minutes
Step-by-step explanation:
You need to first subtract 9 from 11 and you get 2 minutes.
11 minutes will it take to fill the tub by both hot and cold water faucets.
What is Time?
Time as the progression of events from the past to the present into the future.
Given that,
the cold water faucet can fill the tub in 9 minutes
The hot water faucet can fill the tub in 11 minutes.
If both the faucets are used together then it takes 11 minutes to fill the tub because it takes longer time for hot water faucet to fill the tub.
Therefore it takes 11 min to fill the tub together.
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Solve the equation.
y + 3 = -y + 9
y= 1
y=3
y = 6
y = 9
Answers
Answer: y=3
Step-by-step explanation:
To solve the equation, we want to get the same terms onto the same side and solve.
y+3=-y+9 [add y on both sides]
2y+3=9 [subtract 3 on both sides]
2y=6 [divide 2 on both sides]
y=3
Answer:
y=3
Step-by-step explanation:
Line d is parallel to line c in the figure below. Parallel lines d and c are intersected by lines q and p to form 2 triangles. At lines d and p, the angle is 2, at d and q, the angle is 1, and at q and p the angle is 3. At lines c and q, the angle is 4, at p and c, the angle is 5, and the third angle is 6. Which statements about the figure are true? Select three options. Vertical angles prove that Angle 2 is congruent to angle 5. In the two similar triangles, Angle 1 and Angle 4 are alternate interior angles. Vertical angles prove that Angle 3 is congruent to angle 6. The triangles are similar because alternate interior angles are congruent. In the two similar triangles, Angle 2 and Angle 4 are corresponding angles. The triangles are similar because corresponding sides are congruent.
Answers
Answer:
A B C
Step-by-step explanation:
Answer:
abc or 123
Step-by-step explanation:
Part A: Factor 3x2c2 + 5xc2 − 2c2. Show your work. (4 points) Part B: Factor x2 + 6x + 9. Show your work. (3 points) Part C: Factor x2 − 9. Show your work. (3 points) (10 points)
Answers
Answer:
[tex]\boxed{\mathrm{view \: explanation}}[/tex]
Step-by-step explanation:
A) 3x²c² + 5xc² - 2c²
Factor c² from all terms in the expression.
c²(3x² + 5x - 2)
Factor 3x² + 5x - 2
c²(3x-1)(x+2)
B) x² + 6x + 9
x² + 3x + 3x + 9
Factor common terms.
x(x+3)+3(x+3)
Take x+3 common.
(x+3)(x+3)
C) x² - 9
x² -3²
Apply formula : a² - b² = (a+b)(a-b)
(x+3)(x-3)
Answer:
A) [tex]c^2(3x-1)(x+2)[/tex]
B) [tex](x+3)(x+3)[/tex]
C) [tex](x+3)(x-3)[/tex]
Step-by-step explanation:
Part A:
[tex]3x^2c^2+5xc^2-2c^2[/tex]
Taking [tex]c^2[/tex] common
[tex]c^2(3x^2+5x-2)[/tex]
Using mid term break formula
[tex]c^2 (3x^2+6x-x-2)[/tex]
[tex]c^2[3x(x+2)-1(x+2)][/tex]
[tex]c^2(3x-1)(x+2)[/tex]
Part B:
[tex]x^2 + 6x + 9.[/tex]
[tex](x)^2+2(x)(3)+(3)^2[/tex]
[tex](x+3)^2[/tex]
[tex](x+3)(x+3)[/tex]
Part C:
[tex]x^2-9[/tex]
[tex](x)^2-(3)^2[/tex]
[tex](x+3)(x-3)[/tex]
Which of the following steps indicates the distributive property when solving –3(x + 2) = 21?
Question 4 options:
A)
–3x + 2 = 21
B)
–3x – 6 = 21
C)
D)
–3x – 6 = –63
Answers
Answer:
B) –3x – 6 = 21
Step-by-step explanation:
Well the distributive property is the multiplying of a number by more numbers in parenthesis.
For example -3(x + 2) by using the distributive property we get,
-3x - 6
Thus,
the answer is B) -3x - 6 = 21 because it shows the aftermath of the distributive property.
Hope this helps :)
When distributive property applies on 3(x + 2) = 21 expression than it changes as 3x + 6 = 21.
What is distributive property?Distributive property explains us how to solve expressions in the form of a(b + c).
After apply distributive property this term convert as ab+ac.
The given expression is,
3(x + 2) = 21
To solve the expression, use distributive property,
According to distributive property,
a(b + c) changes in the form of ab+ac.
Solve for the given expression,
3x + 2×3 = 21
3x + 6 = 21
Solve for the value of x,
3x = 21 - 6
3x = 15
x = 5
Hence, option (C) is correct.
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Suppose that MNO is isosceles with base NM. Suppose also that =m∠N+4x7° and =m∠M+2x29°. Find the degree measure of each angle in the triangle.
Answers
Answer:
m∠N = 51°
m∠M = 31°
m∠O = 98°
Step-by-step explanation:
It is given that ΔMNO is an isosceles triangle with base NM.
m∠N = (4x + 7)° and m∠M = (2x + 29)°
By the property of an isosceles triangle,
Two legs of an isosceles triangle are equal in measure.
ON ≅ OM
And angles opposite to these equal sides measure the same.
m∠N = m∠M
(4x + 7) = (2x + 29)
4x - 2x = 29 - 7
2x = 22
x = 11
m∠N = (4x + 7)° = 51°
m∠M = (2x + 9)° = 31°
m∠O = 180° - (m∠N + m∠M)
= 180° - (51° + 31°)
= 180° - 82°
= 98°
A college graduate is curious about the proportion of graduates who have loan debt 20 years after graduating. Let the proportion of graduates who have loan debt 20 years after graduating be p. If the college graduate wishes to know if the proportion of graduates who have loan debt 20 years after graduating is less than 18%, what are the null and alternative hypotheses?
Answers
Answer: Null Hypothesis [tex]H_{0}[/tex]: p = 0.18
Alternative Hypothesis [tex]H_{a}[/tex]: p < 0.18
Step-by-step explanation: When doing an experiment, first define the hypotheses you want to test. These hypotheses are Null Hypothesis and Alternative Hypothesis
Null Hypothesis is a general assumption and discloses that there is no relationship between the conditions under consideration. It is the hypothesis the researcher is trying to disprove. It is denoted by the symbol [tex]H_{0}[/tex].
For the college graduate curiosity, the hypothesis the graduate is trying to disprove is that the proportion of students who have loan debt after 20 years of graduation is 18%. Then, Null Hypothesis is [tex]H_{0}[/tex]: p = 0.18
Alternative Hypothesis is the a statement describing a relationship between the collected data. It is what researches try to prove and the results are observations of real causes. It is denoted by the symbol [tex]H_{a}[/tex].
For the graduate study, the alternative is that the proportion is less tahn 18% or 0.18. Then, Alternative Hypothesis: [tex]H_{a}[/tex]: p < 0.18
HELP ASAP PLEASE (25 POINTS) Solve and reduce if possible. 5/12 − 7/8 = ?
Answers
Answer:
-11/24
Step-by-step explanation:
5/12 - 7/8
We need to get a common denominator of 24
5/12 *2/2 - 7/8 *3/3
10/24 - 21/24
-11/24
Answer:
-11/24
Step-by-step explanation:
Well to solve 5/12 - 7/8 we need to find the LCM.
12 - 12, 24, 36, 48
8 - 8, 16, 24, 32, 40
So the LCM is 24.
Meaning we need to make both denominators 24.
12*2 = 24 5*2 = 10
10/24
8*3 = 24 7*3 = 21
21/24
10/24 - 21/24
= -11/24
Thus,
the answer is -11/24.
Hope this helps :)
The graph of y=−x+2 is shown below.
Answers
Answer:
What is the question?
Step-by-step explanation:
If a transversal is perpendicular to one of two parallel lines, then it's ________ to the other line. Question 16 options: A) perpendicular B) congruent C) parallel D) supplementary
Answers
Answer: Perpendicular.
Step-by-step explanation:
Suppose that you have two perpendicular lines:
Remember that a line is something like:
y = a*x +b
and two lines are parallel if they have the same slope (a) but a different y-intercept(b)
Then our lines can be:
y1 = a*x + b1
y2 = a*x + b2.
Now, if we have a line:
y = a*x + b
Then a perpendicular line will have a slope equal to -(1/a):
yp = (-1/a)*x + c
So this only depends on the slope, and we know that our two parallel lines have the same slope. So if we construct a transversal line that is perpendicular to one of our lines, it also must be perpendicular to the other line.
Answer:
A
Step-by-step explanation:
There are 45 balloons: 15 are blue; 20 are green; 10 are red. 3 balloons are selected for the float. Leaving your answers in combinatorics format, how many ways can all 3 be selected such that they are the same color.
Answers
Answer: Required number of ways = 1715
Step-by-step explanation:
Given, there are 45 balloons: 15 are blue; 20 are green; 10 are red.
3 balloons are selected for the float.
Number of combinations to select r things out of n things : [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
So, the number of ways to select 3 ballons such that they are the same color = (Ways to select all blue ) x (Ways to select all green ) x (Ways to select all red)
[tex]^{15}C_3+^{20}C_3+^{10}C_3\\\\=\dfrac{15!}{12!\times3!}+\dfrac{20!}{17!\times3!}+\dfrac{10!}{7!\times3!}\\\\=\dfrac{15\times14\times13}{6}+\dfrac{20\times19\times18}{6}+\dfrac{10\times9\times8}{6}\\\\=455+1140+120\\\\=1715[/tex]
Hence, Required number of ways = 1715
Select the correct answer.
Answers
Answer:
C. 5 × 3
Step-by-step explanation:
The order of a matrix is the number of rows and columns that a matrix has. Rows are listed first and columns are listed second. The matrix has 5 rows going across horizontally and 3 columns going down vertically.
So, the order of the matrix is 5 × 3.
Hope that helps.
