Use the figure below for items 6-7.
Х,
8
w
Z
6. If WY + XZ = 28, what is PZ? 'hint: find WY first
7. If XP = 7x - 2 and PZ = 4x + 10, what is XZ?
Answers
WY=16
XZ=12
PZ=6
7.
7x-2=4x+10
3x=12
x=4
XZ=11x+8
XZ=52
Related Questions
In the figure below, if the radius of circle o
is 10, what is the length of diagonal AC of
rectangle OABC?
Answers
Answer:
The length of AC is 10 units
Step-by-step explanation:
In the given circle O
∵ AOCB is a rectangle
∵ OB and AC are the diagonals of the rectangle AOCB
∵ Diagonals of the rectangle are equal in lengths
→ That means OB and AC are equal in lengths
∴ OB = AC
∵ O is the center of the circle
∵ B is a point on the circle
∴ OB is a radius of the circle O
∵ The radius of the circle is 10 units
∴ OB = 10 units
∵ OB = AC
∴ AC = 10 units
∴ The length of AC is 10 units
Factor the expression using the GCF.
42 – 12 =
Answers
The factors of the expression 42 - 12 are 2(21 - 6), 3(14 - 4), 6(7 - 2).
What are GCF and distributive property?The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.
We also know that distributive property states a(b + c) = ab + ac.
Given, We have to factor 42 - 12.
Now, Factors of 12 are 1, 2, 3, 4, 6 and 12.
Factors of 42 are 1, 2, 3, 6, 7, 14, 21 and 42.
Common factors of 12 and 42 are 2, 3 and 6.
So, 42 - 12.
= 2(21 - 6).
= 3(14 - 4).
= 6(7 - 2).
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The factored form of the expression 42 - 12 using the GCF is 6(7 - 2).
To factor the expression 42 - 12 using the greatest common factor (GCF), we need to find the largest number that divides both 42 and 12.
First, let's find the prime factorization of both numbers:
42 = 2 x 3 x 7
12 = 2 x 2 x 3
Now, let's find the common factors:
The common factors are 2 and 3.
Next, let's determine the GCF by multiplying the common factors:
GCF = 2 x 3 = 6
Finally, we can factor out the GCF from the expression:
42 - 12 = 6 x (7 - 2)
Therefore, the factored form of the expression 42 - 12 using the GCF is 6(7 - 2).
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Write an equation of the line in slope-intercept form. (-2, 4) (0 -1)
Answers
Answer:
y=-5/2x+1
Step-by-step explanation:
-1-4 ( -5 )
0- (-2 ) = 0+2 ( 2 )
-5/2
y=-5/2x+b
4=-5/2( -2 ) +b
4= 5+b
Subtract 4 from 5 ( 1 )
b=1
y=-5/2x+1
Hope this helped, Have a Great Day!!
The equation of the line passing from the given points is y = -5x/2-1
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, a line is passing through two points (-2, 4) and (0 -1)
We know that, the equation of a line passing through two points is given by,
y-y₁ = (y₂-y₁/x₂-x₁)(x-x₁)
Therefore,
y-4 = (-1-4)/(0+2)(x+2)
y-4 = -5/2(x+2)
y = -5x/2-5+4
y = -5x/2-1
Hence, The equation of the line passing from the given points is y = -5x/2-1
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Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of grams and a standard deviation of grams while babies born after a gestation period of 40 weeks have a mean weight of grams and a standard deviation of grams. If a -week gestation period baby weighs grams and a -week gestation period baby weighs grams, find the corresponding z-scores. Which baby weighs relative to the gestation period?
Answers
Complete question :
Suppose babies born after a gestation period of 32 to 35 weeks have a mean weight of 2800 grams and a standard deviation of 900 grams while babies born after a gestation period of 40 weeks have a mean weight of 3100 grams and a standard deviation of 410 grams. If a 32 -week gestation period baby weighs 3300 grams and a 40 -week gestation period baby weighs 3600 grams, find the correspondingz-scores. Which baby weighs more relative to the gestation period? Find the corresponding z-scores. Which baby weighs relatively more?
Answer:
32 - 35 weeks = 0.56
40 weeks : 1.22
40 weeks babies weigh more
Step-by-step explanation:
Given that :
32 - 35 weeks babies :
Mean (m) = 2800
Standard deviation (s) = 900
Weight (x) = 3300
40 weeks babies :
Mean (m) = 3100
Standard deviation (s) = 410
Weight (x) = 3600
Obtain the standardized score for both categories :
Zscore = (x - m) / s
32 - 35 weeks :
Zscore = (3300 - 2800) / 900
Zscore = 0.555555 = 0.56
40 weeks :
Zscore = (3600 - 3100) / 410
Zscore = 1.2195121 = 1.22
Zscore for 40 weeks is higher than 32-35 weeks.
Hence, 40 weeks babies weigh more.
√x + 4 +
x + 4 + 2
√x + 4√2
Answers
Answer:
this is the correct answer
5.2.21-T
Question Help
Assume that when adults with smartphones are randomly selected 44%use them in meetings or classes. If 17 adult smartphone users are randomly selected, find the probability that exactly 2 of them use their smartphones in
Meetings or classes
Answers
Answer:
0.004398
Step-by-step explanation:
Given that:
p = 44% = 0.44
Number of trials (n) = 17
Probability that exactly 2 of them use smartphones in meetings or classes =?
Using the binomial probability formula :
P(x = 2)
P(x = x) = nCx * p^x * (1 - p)^(n-x)
P(x = 2) = 17C2 * 0.44^2 * 0.56^15
P(x = 2) = 136 *0.1936 * 0.0001670399
P(x = 2) = 0.00439809
P(x = 2) = 0.004398
for the function g (x) shown graphed below, over which of the following intervals is g (x) > 0
Answers
Answer:
g(-1) is lesser than 0 while h(-1) is -3(-1) + 8 = 11 so g(-1) is lesser than h(-1)
g(1) is 5 while h(1) is -3(1) + 8 = 5 so g(1) is equal to h(1)
Step-by-step explanation:
The function g(x) is greater than zero when the value of x lies in between -3 and 5 and this can be determined by using the given graph.
Given :
The graph of the function g(x) is given.
The following steps can be used in order to determine the interval for g(x):
Step 1 - The value of g(x) means the value of y.
Step 2 - The value of g(x) is positive when the graph of g(x) is in the first or in the second quadrant.
Step 3 - So, according to the graph function g(x) is positive when the value of x is in between -3 and 5.
Therefore, the correct option is 3).
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AI Drew a line that was 3/4 of an inch long. He decided to shorten it and erased 1/4 of an inch of the line. How long was the line that remained express the answer in the lowest terms.
Answers
Answer:
1/2
Step-by-step explanation:
3/4 minus 1/4 is equal to 2/4
2/4 is 1/2
A polling agency is investigating the voter support for a ballot measure in an upcoming city election. The agency will select a random sample of 500 voters from one region, Region A, of the city. Assume that the population proportion of voters who would support the ballot measure in Region A is 0.47. What is the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50
Answers
Answer:
The value is [tex]P( X > 0.50) = 0.089264[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 500
The population proportion is p = 0.47
Generally given that the sample size is sufficiently large , the mean of this sampling distribution is mathematically represented as
[tex]\mu_x = p = 0.47[/tex]
Generally the standard deviation of the sampling distribution is mathematically represented as
[tex]\sigma = \sqrt{\frac{p(1- p )}{ n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{ 0.47 (1-0.47 )}{ 500 } }[/tex]
=> [tex]\sigma = 0.0223[/tex]
Gnerally the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is mathematically represented as
[tex]P( X > 0.50) = P( \frac{ X - \mu }{ \sigma } > \frac{ 0.50 - 0.47 }{ 0.0223 } )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
=> [tex]P( X > 0.50) = P( Z> 1.3453 )[/tex]
From the z table the area under the normal curve to the left corresponding to 1.3453 is
[tex]P( Z> 1.3453 ) = 0.089264[/tex]
So
[tex]P( X > 0.50) = 0.089264[/tex]
Using the normal distribution and the central limit theorem, it is found that there is a 0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
In a normal distribution 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]
It 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, which is the percentile of X.
By the Central Limit Theorem, the sampling distribution of sample proportions of size n of a proportion p has [tex]\mu = p, s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this problem:
Sample of 500 voters, hence [tex]n = 500[/tex].The proportion is of 0.47, hence [tex]p = 0.47[/tex]The mean and the standard deviation are:
[tex]\mu = p = 0.47[/tex]
[tex]\sigma = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.47(0.53)}{500}} = 0.0223[/tex]
The probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50 is 1 subtracted by the p-value of Z when X = 0.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.47}{0.0223}[/tex]
[tex]Z = 1.34[/tex]
[tex]Z = 1.34[/tex] has a p-value of 0.9099.
1 - 0.9099 = 0.0901
0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
A similar problem is given at https://brainly.com/question/24663213
sam was charged $1050 in interest on a loan with a 2.5% interest rate. what was the original amount of the loan if he took 5 years to pay it back?
Answers
Answer:
$918.75
Step-by-step explanation:
2.5 ÷ 100 = 0.025 × 1050 = 26.25
26.25 × 5 = 131.25
1050 - 131.25 = 918.75
Which algebraic representation of a transformation on a coordinate grid does not preserve congruence A (x,y)-(x+6,y+6 .B(x,y)-(-x,y)C(x,y)-(6x,6y)D(x,y)-(-y,x)
Answers
Answer:
It’s A
Step-by-step explanation:
Can someone help me explain please?
Answers
Answer:
B. 16 = 4y
y = 4
Answer:
B. 16 = 4y
Step-by-step explanation:
Long block = 16Amount of blocks that make the long block (16): 4Label of the small blocks: yTotal of small blocks: y × 4y × 4 = 4yBecause the long block and the y blocks are equal, 16 = 4yI hope this helps!
Antonio completed the right column of the table to help him find the sum of 2/9 and 1/5.
Answers
Answer:
Step 1 is the first error
Step-by-step explanation:
Given
[tex]\frac{2}{9} + \frac{1}{5}[/tex]
Required
Which step contains the first error?
From the attachment, the first step is the first error.
This is so because the fractions can not be written as a fraction with a denominator of 14
Solving further:
[tex]\frac{2}{9} + \frac{1}{5}[/tex]
Find Common Denominator 45
[tex]\frac{2*5}{9*5} + \frac{1*9}{5*9}[/tex]
[tex]\frac{10}{45} + \frac{9}{45}[/tex]
Add:
[tex]\frac{10 + 9}{45}[/tex]
[tex]\frac{19}{45}[/tex]
This is from the same project that I was struggling with and was similar to the other problem but I couldn't figure it out.
Answers
9514 1404 393
Answer:
y = -1/4x^2 -3/2x +3/4
Step-by-step explanation:
You know that vertex form is ...
y = (1/(4p))(x -h)^2 +k
for a focus-vertex distance of p and a vertex of (h, k).
Here, the focus-vertex distance is 2-3 = -1 (difference of y-coordinates), and the vertex is (h, k) = (-3, 3). This means the vertex form equation is ...
y = -1/4(x +3)^2 +3
Expanding the square gives ...
y = -1/4(x^2 +6x +9) +3
y = -1/4x^2 -3/2x +3/4
_____
Additional comment
The square of a binomial is ...
(x +a)^2 = x^2 +2ax +a^2
the temperature of the coffee depends on the number of minutes it sits on the desk
Answers
Answer:
um D I really hope this helps
Step-by-step explanation:
: a p e x
what’s the slope?
the line has the given equation y+7=3/5(x-4)
Answers
Answer:
Slope 3/5
Step-by-step explanation:
y=3/5x-47/5
can someone help please
Answers
It’s 8:40 What time will it be in 3/4 hour
Answers
Answer: 9:25
Step-by-step explanation:
In a car race, for every mile covered by car A, car B covered 4 miles. The ratio of the number of miles covered by car A to the number of miles covered by car B is ___.
Real answer please
Answers
who is willing to help me with my work for money ?
Answers
Answer:
sure, but not sure if this is allowed on brainly...
also this is just tutoring
Brianna hoped to get 100 pumpkins from her garden this year. Since the weather was really great, 20% more pumpkins grew than expected. Unfortunately, animals ate 30% of all the pumpkins that grew.
How many pumpkins were left?
Answers
9514 1404 393
Answer:
84
Step-by-step explanation:
Assuming that "hoped for" and "expected" are the same number, The number Brianna has remaining is ...
100(1 +20%)(1 -30%) = 100(1.2)(0.7) = 100(0.84) = 84
84 pumpkins were left.
okay last one haha i promise
Answers
Answer:
B) x = -2 or x = 3/5
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Standard Form: ax² + bx + c = 0FactoringSolving RootsStep-by-step explanation:
Step 1: Define
5x² + 7x = 6
Step 2: Solve for x
Rewrite [SF]: 5x² + 7x - 6 = 0Factor: (x + 2)(5x - 3) = 0Find roots: x = -2, 3/5Montel has a circular garden with a diameter of 12 feet. He purchases
border stones for the circumference of his garden. Each border stone is 1 foot long. How many border stones should Montel buy?
Answers
PLSS HELPP FOR 20 POINTS!!
Answers
The students at Southern Junior high School are divided into four home rooms. Benjamin just moved into the school district and will be randomly assigned to one home room
Answers
Answer:
A 4 side dice.
Step-by-step explanation:
Benjamin has 4 possible homerooms with the same probability. This means that every homeroom has a 1/4 = 0.25 (or 25%) probability of getting chosen.
You could emulate this situation with a 4 sided dice (are like little pyramids) where each side of the dice would represent the selection of one of the homerooms.
help solve for me please
Answers
Answer:
A''=(8,0)
B''=(12,-5)
C''=(16,-4)
D''=(17,3)
Step-by-step explanation:
Translations
The following points are given:
A=(2,3)
B=(6,-2)
C=(10,-1)
D=(11,6)
Two transformations will be applied:
T(x,y)->(x+12,y-8). It means: add 12 to x, subtract 8 to y
T(x,y)->(x-6,y+5). It means: subtract 6 to x, add 5 to y
Start with point A. First translation:
A'=(2+12,3-8)=(14,-5). Second translation:
A''(14-6,-5+5)=(8,0)
Now for point B. First translation:
B'=(6+12,-2-8)=(18,-10). Second translation:
B''(18-6,-10+5)=(12,-5)
Now for point C. First translation:
C'=(10+12,-1-8)=(22,-9). Second translation:
C''(22-6,-9+5)=(16,-4)
Finally for point D. First translation:
D'=(11+12,6-8)=(23,-2). Second translation:
D''(23-6,-2+5)=(17,3)
-2( 4 - 3n) answer pleseeewwwwew
Answers
Answer:
The answer is 6n - 8. if right, your welcome.
Factor 140c+28-14a to identify the equivalent expressions.
Answers
Answer:
Answer is A,C, and D
Step-by-step explanation:
write a similarity statement for the triangles picture. what is the value of x? show your work please !
Answers
Answer:x= 16.5
Step-by-step explanation:as both the triangles are similar, then
AB/ PQ=AC/ PR
16/24=18/(2x-6)
x= 16.5
You deposit $2200 in the account that pays 3% annual interest compounded continuously after 20 years you withdraw the money what formula do you use
Answers
Answer: 6600
Step-by-step explanation:
To find the original price, first we need to answer, \$\greenD{1.54}$1.54dollar sign, start color #1fab54, 1, point, 54, end color #1fab54 is \blueD{5.5}\%5.5%start color #11accd, 5, point, 5, end color #11accd, percent of what number?
Hint #22 / 5
Percent means per hundred, so \blueD{5.5}\%5.5%start color #11accd, 5, point, 5, end color #11accd, percent is equivalent to \blueD{\dfrac{5.5}{100}}
100
5.5
start color #11accd, start fraction, 5, point, 5, divided by, 100, end fraction, end color #11accd which is also equal to \blueD{5.5\div 100}5.5÷100start color #11accd, 5, point, 5, divided by, 100, end color #11accd.
\blueD{5.5 \div 100 = 0.055}5.5÷100=0.055start color #11accd, 5, point, 5, divided by, 100, equals, 0, point, 055, end color #11accd
Hint #33 / 5
To find the original price, we need to know \blueD{0.055}0.055start color #11accd, 0, point, 055, end color #11accd times what number equals \greenD{1.54}1.54start color #1fab54, 1, point, 54, end color #1fab54.
\blueD{0.055} \maroonD{x} = \greenD{\$1.54}0.055x=$1.54start color #11accd, 0, point, 055, end color #11accd, start color #ca337c, x, end color #ca337c, equals, start color #1fab54, dollar sign, 1, point, 54, end color #1fab54
Hint #44 / 5
\begin{aligned} \blueD{0.055} \maroonD{x} &= \greenD{\$1.54} \\\\ \dfrac{\blueD{0.055} \maroonD{x}}{\blueD{0.055}} &= \dfrac{\greenD{\$1.54}}{\blueD{0.055}} \\\\ \maroonD{x} &= \maroonD{28} \end{aligned}
0.055x
0.055
0.055x
x
=$1.54
=
0.055
$1.54
=6600