The value of the expression when evaluated is: 162.
How to Evaluate an Expression?To evaluate the expression, 6x^4y^3, substitute x = -1 and y = 3 into the expression and solve.
6(-1^4) × 3^3
6(1) × 27
6 × 27
162
The value of the expression, 6x^4y^3, is: 162.
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Add: -5x + (3x-8)
answer asap if possible pls
Answer:
-2x-8
Step-by-step explanation:
-5x + (3x-8)
-5x +3x -8
-2x - 8
Answer:
-2x-8
Step-by-step explanation:
-5x+(3x-8)
-5x+3x-8
-2x-8
Try this
When two births are randomly selected, the sample space for genders is bb, bg, gb, and gg. Assume that those four outcomes are equally likely. Construct a table that describes the sampling distribution of the sample proportion of girls from two births. Does the mean of the sample proportions equal the proportion of girls in two births? does the result suggest that a sample proportion is an unbiased estimator of a population proportion? for the entire population, assume the probability of having a boy is , the probability of having a girl is , and this is not affected by how many boys or girls have previously been born.
The probability illustrates that the mean of the sample proportions equal the proportion of girls in two births.
How to calculate the probability?The table that describes the sampling distribution of the sample proportion of girls from two births will be:
Girls Probability
0. 0.25
0.5. 0.5
1. 0.25
The mean of the sample proportions equal the proportion of girls in two births. This is illustrated as 1/2.
Also, the result suggest that the sample proportion is an unbiased estimator big the population proportion because rye sample proportion and population proportion are not the same.
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Identify the equivalent expression of z + z + z + z
4z
4 + z
2z
3z
The Answer Is:
4z
Hope this helped!
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\large\textbf{Identify the equivalent expression z + z + z + z}\downarrow[/tex]
[tex]\huge\textbf{Let's find out which one is equal to}\\\\\huge\textbf{the following expressions:}[/tex]
[tex]\large\textbf{z + z + z + z}[/tex]
[tex]\large\textbf{= 1z + 1z + 1z + 1z}[/tex]
[tex]\large\textbf{= 2z + 1z + 1z}[/tex]
[tex]\large\textbf{= 3z + 1z}[/tex]
[tex]\large\textbf{= 4z}[/tex]
[tex]\huge\textbf{Anwer:}[/tex]
[tex]\huge\boxed{\textsf{Option A. 4z}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Is it possible to have a polygon whose sum of the interior angles is 850 degrees
Answer: No
Step-by-step explanation:
The sum of the interior angles of a polygon with n sides is given by [tex]180(n-2)[/tex]. Setting this equal to 850 degrees,
[tex]180(n-2)=850\\\\n-2=\frac{85}{18}\\\\n=\frac{121}{18}[/tex]
Since this gives n to be a non-integer value, this is an impossible situation since a polygon must have an integer number of side lengths.
Is this graph a function ?
Please help
Answer:
Yes
Step-by-step explanation:
To find out whether or not a graph is a function, we can do the vertical line test. If the vertical line only touches one point, then the graph is a function. This is because in a function, an input can only have one output.
x/4+7=27 what is x? how do i find x if it is in a fraction?
Answer:
x=80
Step-by-step explanation:
So normally when x is in the numerator, you multiply both sides of the equation by whatever the denominator is to cancel out the fraction. But in this case since you don't have the fraction alone, you normally want to isolate it first So let's do that
Original equation:
[tex]\frac{x}{4}+7=27[/tex]
Subtract 7 from both sides
[tex]\frac{x}{4}=20[/tex]
Multiply both sides by 4 to cancel out the denominator:
[tex]x=80[/tex]
The sum of Andys, James, and Declans age is 33. What will the sum their ages in 3 years
Answer:
one hundred and two years
Answer:
42
Step-by-step explanation:
Each ages at the same rate. In 3 years, all will be 3 years older.
ApplicationThe sum of their ages now is ...
A +J +D = 33
In 3 years, the sum will be ...
(A +3) +(J +3) +(D +3) = (A +J +D) +(3 +3 +3) = 33 +9 = 42
In 3 years, the sum of their ages will be 42.
What is the measure of ∠D?
Answer:
28°Step-by-step explanation:
the triangles are similar, so same angles
the sum of the interior angles of a triangles is 180°
take away from 180° the know angles and you will have your answer
180 - 62 - 90 =
28°
Two mechanics worked on a car. the first mechanic worked 10 hours the second mechanic worked for 15 hours together
The rate charged by first mechanic is $45 per hour and the rate charged by second mechanic is $50 per hour.
Given mechanic first worked 20 hours and mechanic second worked 15 hours and they charged $1650. The sum of rates of first mechanic and second mechanic is $95 per hour.
let the rate charged by first mechanic be x .
let the rate charged by second mechanic be y.
According to question
x +y=95-----------1
20x+15y=1650----------2
Multiply equation 1 by 20 and subtract equation 2 from 1.
20x+20y-20x-15y=1900-1650
5y=250
y=50
put the value of y=50 in 1 to get the value of x.
x +y=95
x+50=95
x=95-50
x=45
Hence the rate charged by first mechanic is $45 per hour and the rate charged by second mechanic is $50 per hour.
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Question is incomplete as it should be as under:
Two mechanics worked on a car, the first mechanic worked 20 hrs. and the second mechanic worked 15 hours together. They charged a total of $ 1650. What is the rate charged per hour for each mechanic if the sum of the two rates per hour was $95 per hour?
What is the midpoint of the line segment given endpoints (-9,1) and (-5,-9)
Answer:
Hello! The answer to your question is (-7, -4).
Step-by-step explanation:
To solve this problem, you have to use the midpoint formula:
[tex](\frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]
Now, we can substitute our values in:
[tex](\frac{-9 + -5}{2}, \frac{1 - 9}{2} )\\= (\frac{-14}{2} , \frac{-8}{2}) \\= (-7, -4)[/tex]
A 2-column table with 7 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries 15, 0, 3, 0, negative 3, 0, 15.
Predict which statements are true about the intervals of the continuous function. Check all that apply.
f(x) > 0 over the interval (−, 3).
f(x) ≤ 0 over the interval [0, 2].
f(x) < 0 over the interval (−1, 1).
f(x) > 0 over the interval (–2, 0).
f(x) ≥ 0 over the interval [2, ).
The true statements about the function are:
f(x) ≤ 0 over the interval [0, 2].f(x)>0 over the interval (-2,0)f(x) ≥ 0 over the interval [2,∞)How to determine the true statement?The table of values is given as:
x f(x)
-3 -15
-2 0
-1 3
0 0
1 -3
2 0
3 15
From the table, the function values do not exceed 0 at the interval 0 to 2.
This means that f(x) ≤ 0 over the interval [0, 2].
Also from the table, the function values exceeds 0 at the intervals greater than -2 but less than 0
This means that f(x)>0 over the interval (-2,0)
Also from the table, the function values are at least 0 at the intervals greater than 2
This means that f(x) ≥ 0 over the interval [2,∞)
Hence, the true statements are (b), (d) and (e)
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Answer:
The answers are B, C, and D
Step-by-step explanation:
Edge 2023
Can someone pls help me?
I'm not sure how to convert a logarithm to natural logarithm.
only (a)
Answer:
[tex] \frac{2 ln(5) }{3 ln(2) } [/tex]
Step-by-step explanation:
[tex] log_{8}(25) = \frac{ ln(25) }{ ln(8) } = \frac{ ln( {5}^{2} ) }{ ln( {2}^{3} ) } = \frac{2 ln(5) }{3 ln(2) } [/tex]
If Gabriel takes a 25 question multiple choice test and receives a score of 52%, how many questions did he answer correctly
Answer: 13 questions
Step-by-step explanation:
52% of 25 is 13
25/x=100%/52%
x=13
Given the six rational numbers below, come up with the greatest sum, difference, product,
and quotient, using two of the numbers for each operation.
-5 1/2
3.75
-20.8
8
-4
11 1/4
The greatest sum, difference, product and quotient is 9, 12, 90 and 26 respectively.
How to determine the operationsGiven the numbers -5 1/2, 3. 75, -20. 8, -4, 11 1/4
a. SUM
=8 + [tex]11* \frac{1}{4}[/tex]
= [tex]8 + \frac{45}{4}[/tex]
= [tex]\frac{32 + 4}{4}[/tex]
= [tex]\frac{36}{4}[/tex]
= 9
B. Difference
= 8 - (-4)
= 8 + 4
= 12
C. Product
= [tex]8 * \frac{45}{4}[/tex]
= [tex]2 * \frac{45}{1}[/tex]
= 90
D. Quotient
= [tex]8 * 3. 25[/tex]
= 26
Thus, the greatest sum, difference, product and quotient is 9, 12, 90 and 26 respectively.
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HELP HELP HELP HELP HELP
Answer:
3√5 or ≈ 6.71
Step-by-step explanation:
The Distance Formula is d = √((x2-x1)² + (y2-y1)²)
Given Points: (-3, 2) and (0, -4)
Points: (x1, y1) and (x2, y2)
Find the difference between coordinates:
(x2 - x1) = (0 - (-3)) = 3
(y2-y1) = (-4 - 2) = -6
Square the results and sum them up:
(3)² + (-6)² = 9 + 36 = 45
Now Find the square root and that's your result:
Exact solution: √45 = 3√5
Approximate solution: 6.7082
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Which ordered pair comes from the table ?
Answer:
B
Step-by-step explanation:
The only x,y pair in the table is 4,2
What values of a and b make this equation true?
Answer:
a = -4
b=-29
Step-by-step explanation:
Complex number:First write the radicals in simplest form.
i² = -1
[tex]\sf (4 + \sqrt{-49}) -2\left(\sqrt{(-4)^2}+\sqrt{-324}\right)=4 + \sqrt{49i^2} - 2\left(\\\sqrt{16}+\sqrt{324i^2}\right)[/tex]
[tex]\sf =4 + \sqrt{7*7*i*i}-2\left(\sqrt{4*4}+\sqrt{18*18*i*i}\right)\\\\= 4 + 7i - 2(4 + 18i)\\\\= 4 + 7i - 2*4 - 2*18i\\\\= 4 + 7i -8-36i\\\\= 4 - 8 +7i - 36i\\\\= -4 - 29i[/tex]
[tex]\sf \boxed{a = -4 }\\\\\boxed{b=-29}[/tex]
1. Annie and her friends are playing a game called Doubles. In the game, a player
rolls two number cubes at the same time. The outcome of each roll is the sum of the
two number cubes. Extra points are scored for rolling doubles the same number
on both number cubes.
-
Part A: Complete this table to show the sample space for each roll in the game. (6
points)
HELP ASAP WILL GIVE BRAINLIEST!!!!
Answer:
There are 6 possible outcomes for die A and 6 possible outcomes for die B.
Each of the 6 outcomes of die A can be combined with each of the 6 outcomes of die B. Therefore the total number of possible outcomes for each roll is given by:
6*6=36
Find the first four terms of the sequence given by the following. an=6 x (-4)^n-1, n= 1, 2, 3...
The first four terms of the sequence are 6, -24, 96 and -384
How to determine the first four terms?
The sequence is given as:
an=6(-4)^n-1
When n = 1, we have:
a(1)=6(-4)^(1-1)
This gives
a(1) = 6
When n = 2, we have:
a(2)=6(-4)^(2-1)
This gives
a(2) = -24
When n = 3, we have:
a(3)=6(-4)^(3-1)
This gives
a(3)=96
When n = 4, we have:
a(4)=6(-4)^(4-1)
This gives
a(4)=-384
Hence, the first four terms of the sequence are 6, -24, 96 and -384
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Write a formula that will help Eli determine
how much money he will earn in one week.
Let's let
a = total amount earned
h = hours worked in one week
n = number of items repaired
b = bonus amount for each item
Use the curved parenthese '()', if required.
Do not use other parentheses like '{}' or '[]'.
The formula that will help eli determine how much money he will earn in one week is a = 9h + nb
FormulaLet
a = total amount earnedh = hours worked in one weekn = number of items repairedb = bonus amount for each itemAmount earned per hour = $9a = (9 × h) + (n × b)
a = 9h + nb
Complete question:
Eli works in an electronics repair shop. he earns 9 dollars an hour plus a bonus for each item her repairs.
write a formula that will help eli determine how much money he will earn in one week
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What is the measure of this line?
80 mm
840mm
84mm
80.4 mm
Answer:
84 mm
Step-by-step explanation:
1 cm = 10 mm
8.4 cm = 84 mm
a water tank contains 200 gallons before water is added at a constant rate for six hours until there is 500 gallons in the tank. the faucet is then turned off and the plug is removed so that the tank loses all of its water in over a 10 hour period. write an absolute value function that models the amount of water in the tank V(t) in terms of elapsed time, (t) then state it’s domain.
Answer:
200+500
Step-by-step explanation:
its wrong i answered the wrong question
To enroll in a 30 hour spanish class, students must pay $480.50. If the language center collected a total of $19,260, how many people enrolled in the Spanish class?
Answer:
40 people
Step-by-step explanation:
480.80 times 40 this equals 19,220
Which expression is equivalent to 6^-3?
1/216 is the equivalent expression for the given exponent [tex]6^{-3}[/tex].
An algebraic expression is a mathematical expression involving mathematical operations, variables, numbers, and mathematical quantities and combinations of them.
A negative exponent is the reciprocal of the same exponent with a positive value.
The reciprocal of any number is given by the fraction with the number as denominator and 1 as the numerator.
Here the given negative exponent is given by,
[tex]6^{-3}[/tex]
The exponent with positive value of the given negative exponent is given by [tex]6^3[/tex]
Reciprocal of the above exponent with positive value is given by,
[tex]\frac{1}{6^3}[/tex]
So now Calculating the negative exponent we have,
[tex]6^{-3} = \frac{1}{ {6}^{3} } = \frac{1}{216} [/tex]
Hence the equivalent expression for the given negative exponent is 1/216.
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convert (-6, pi/2) into rectangular coordinates
The conversion of (6, pi/2) from polar into rectangular coordinates is (0, 6)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The conversion from polar to rectangular coordinates is:
x = rcosФ and y = rsinФ
Hence:
x = 6cos(π/2) = 0, y = 6sin(π/2) = 6
The conversion of (6, pi/2) from polar into rectangular coordinates is (0, 6)
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Triangle QRS is dilated according to the rule DO,2 (x,y).
On a coordinate plane, (0, 0) is the center of dilation. Triangle Q R S has points (negative 3, 3), (2, 4), and (negative 1, 1).
What is true about the image ΔQ'R'S'? Select three options.
Which statements are true?
DO,2 (x,y) = (2x, 2y)
Side Q'S' lies on a line with a slope of -1.
QR is longer than Q'R'.
The vertices of the image are closer to the origin than those of the pre-image.
The distance from Q' to the origin is twice the distance from Q to the ori
The correct options about the dilation are; Options A, B and E
How to interpret Dilated Objects?
From the given information, find attached a dilated image.
The scale factor is 2
QRS → Q'R'S' = (x,y) → 2(x,y)
The coordinates of ∆QRS are; Q (-3, 3), R (2, 4) and S (-1, 1)
To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In other words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.
2(x, y) = (2x, 2y)
The coordinates of ∆Q'R'S' becomes: Q' (-6, 6), R' (4, 8), S' (-2, 2)
To determine the statements that are true about the image ΔQ'R'S,
Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.
A) DO, 2 (x, y) = (2x, 2y)
A dilation about the origin with a scale factor 2 is described using the above notation.
Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)
R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)
S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)
Thus Option A is correct.
B) Side Q'S' lies on a line with a slope of -1
Q' (-6, 6)
S' (-2, 2)
coordinate (x, y)
Slope = m = (change in y)/(change in x)
m = (6-2)/[-6-(-2)]
m = 4/(-6+2) = 4/-4
m = -1
Option B is correct
c) QR is longer than Q'R'
Length of QR (-3 to 2) = 5
Length of Q'R' (-6 to 4) = 10
QR is not longer than Q'R'
Option C is false
d) The vertices of the image are closer to the origin than those of the pre-image.
From the diagram, the vertices of the preimage are closer to the origin than those of the dilation image.
Option D is False
e) The distance from Q' to the origin is twice the distance from Q to the origin.
The distance from Q' to the origin (6 to 0) = 6
The distance from Q to the origin (3 to 0) = 3
The distance from Q' to the origin = 2(the distance from Q to the origin)
Option E is correct.
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If sin theta < 0 and tan theta > 0 then
If sin theta < 0 and tan theta > 0 as described in the task content, then, cos theta < 0 and 180<theta <270.
What is correct about angle theta as described?From the task content, it was described that sin theta < 0 and tan theta > 0.
Upon recall of angle quadrants, it follows that only the 3rd quadrant angles have positive tan values and negative sin values. Hence, it follows that the angle theta is in the 3rd quadrant and also has cos theta < 0.
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Suppose 40% of American singers are Grammy award winners. If a random sample of size 743 is selected, what is the probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%
Using the normal distribution, it is found that there is a 0.905 = 90.5% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The proportion and the sample size are given, respectively, by:
p = 0.4, n = 743
Hence the mean and the standard error are given, respectively, by:
[tex]\mu = p = 0.4[/tex][tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.4(0.6)}{743}} = 0.018[/tex]The probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3% is the p-value of Z when X = 0.43 subtracted by the p-value of Z when X = 0.37, hence:
X = 0.43:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.43 - 0.4}{0.018}[/tex]
Z = 1.67
Z = 1.67 has a p-value of 0.9525.
X = 0.37:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.37 - 0.4}{0.018}[/tex]
Z = -1.67
Z = -1.67 has a p-value of 0.0475.
0.9525 - 0.0475 = 0.905.
0.905 = 90.5% probability that the proportion of Grammy award winners will differ from the singers proportion by less than 3%.
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An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 13 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 30 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds. The test statistic for this hypothesis would be __________.
The test statistic for the hypothesis would be 1.413.
Given that the participants in its new diet program lose, on average, more than 13 pounds and the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds.
The objective is to text the advertisement's claim that participants in new diet program lose weight, on average, more than 13 pounds.
Hypothesis:
Null hypothesis:H₀:μ=13
Alternative hypothesis:Hₐ:μ>13
Here, μ be the mean weight loss of all participants.
n=30,
Degree of freedom n-1=30-1=29
[tex]\bar{x}[/tex]=13.8 and s=3.1
To test the null hypothesis H₀, the value of test static would be calculated as follows:
[tex]\begin{aligned}t&=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\\ t_{29}&=\frac{13.8- 13}{\frac{3.1}{\sqrt{30}}}\\ &=\frac{0.8}{0.566}\\ &=1.413\end[/tex]
Hence, the value of the test static for the hypothesis with the mean weight loss of these participants as 13.8 pounds with a standard deviation of 3.1 pounds is 1.413.
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Help ASAP pls
Which of the following statements is true?
B
A
D
E
C
A. the segment BD bisects segment EC
B. segment AC is a perpendicular bisector
C. the segment DE is perpendicular to segment AC
D. the segment BD should be parallel to segment AE
the segment DE is perpendicular to segment AC
==========================================================
Explanation:
The tiny square marker indicates we have a 90 degree angle, which in turn means the two segments DE and AC are perpendicular.
Furthermore, DE is a perpendicular bisector of AC because AC is broken into two equal pieces (AE and EC). The term "bisect" means "split in equal halves". We know that AE = EC due to the small tickmarks on each mentioned segment.
Choice B states "AC is a perpendicular bisector". This is incorrect because AC does not split any segments into two equal pieces. If choice B said "DE is a perpendicular bisector", then it would be correct.