None of the values in the given set makes the inequality false.
Given that,
To check for the expression 5m/6 - 5 < m/2 + 3, whether the set of values S:{−24, 2, 20, 35} holds or not.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
given expression,
5m/6 - 5 < m/2 + 3
5m/6 - m/2 < 3 + 5
(5m - 6m)/6 < 8
-m < 48
m > -48
Thus, none of the values in the given set make the inequality false.
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Juan has a piano recital next month. Last week he practiced for 4 hours in the morning and 9 hours in the afternoon. A full practice session is 2 hours long. How many full practice sessions does Juan complete?
The length of the base of an isosceles triangle is x. The length of a leg is 4x-3. The perimeter of the triangle is 129 Find x.
The value of x in the given isosceles triangle is x = 15
Perimeter of an isosceles triangle: Calculating the value of xFrom the question, we are to determine the value of x.
From the given information,
The length of the base of the isosceles triangle is x
Also,
The length of a leg is 4x - 3
Since, the length of the legs of an isosceles triangle are equal,
Then,
The length of the other leg is 4x - 3
Also, form the given information,
The perimeter of the triangle is 129
Thus,
x + 4x - 3 + 4x - 3 = 129
Now, solve for x
x + 4x - 3 + 4x - 3 = 129
Collect like terms
x + 4x + 4x = 129 + 3 + 3
9x = 135
Divide both sides by 9
9x/9 = 135/9
x = 15
Hence, the value of x is 15
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Please graph this equation y=4|x-1|+3
The graph of equation y=4|x-1|+3 is as shown below.
In this question, we need to graph the equation y=4|x-1|+3
We know that the parent function of given equation is z = |x|
A parent function is translated right by 1 unit then it is dilated vertically by 4 units and the resulting image is translated up by 3 units.
The graph of equation y=4|x-1|+3 is as shown below.
The vertex of equation y=4|x-1|+3 is at (1, 3)
Therefore, the graph of equation y=4|x-1|+3 is as shown below.
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At the local petting zoo, 65% of the goats are female. A researcher selects a sample of five and the goats and notes that three are female. What are p nd p^(p-hat) for female goats?
The values of p and ρˆ (p-hat) in the sample are
p = 0.65 and ρˆ (p-hat) = 0.4
How to determine the values of p and ρˆ (p-hat)?From the question, we have the following parameters that can be used in our computation:
Proportion of female goats = 65%
Sample = 5
Female = 3
The proportion of female represents the variable p
So, we have
p = Proportion of female = 65%
This gives
p = 65%
Express as decimal
p = 0.65
The variable ρˆ (p-hat) is then calculated as
ρˆ = x/n
In this case,
x = Female = 2
n = Male + Female = 2 + 3 = 5
So, we have
ρˆ = 2/5
Evaluate
ρˆ = 0.4
Hence, the values are 0.48 and 0.44, respectively
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The approximate average distances from the sun to Mars and Mercury are listed below:
Mars: 2.28\times 10^{8}2.28×10
8
kilometers
Mercury: 5.79\times 10^{7}5.79×10
7
kilometers
How much farther from the sun is Mars? Express your answer using scientific notation?
The distance from the Sun to Mars is 3. 9 times farther
What is ratio?Ratio can be described as a mathematical comparison between two or more numbers or elements in relation to each other on the basis of their sizes or magnitudes.
It is however known to show how many times one number or elements contains another.
Based on the information given, we have;
Distance from the Sun to Mars = 2.28×10^8Distance from the Sun to Mercury = 5.79×10^7To determine the ratio of their distances from the Sun, we have;
Distance from the Sun to Mars /Distance from the Sun to Mercury
Substitute the values
2.28×10^8/5.79×10^7
Divide through
3. 9 times
Hence, the distance is 3. 9 times farther.
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Kelly went to a store to purchase a coffee pot. She will use a coupon for 20% off. She can calculate the cost before sales tax using the following expression, where c represents the original cost of the coffee pot.
c−0.2c
Which other expression could Kelly use to calculate her cost before sales tax?
Answer:
0.2c-c
Step-by-step explanation:
The weight of four different boxes is shown in pounds. Which list shows the weights in order from least to greatest?
16.4, 16 1/2, 16.625 , 16 3/5
Answer: 16.4, 16 1/2, 16 3/5 16.625,
Step-by-step explanation: 16.4, 16 1/2, 16 3/5 16.625,
16 1/2 = 16.5, 16 3/5 = 16.6
Which ordered pair gives a solution of the system of equations represented in
the graph below?
A. (-1.5, 2.5)
B. (-2.5, 1.5)
C. (2.5, -1.5)
D. (2.5,1.5)
Answer: The correct answer is D. (2.5,1.5)
Step-by-step explanation:
As noted in the graph, the lines intersect at the location where x=2.5 and y=1.5 in Quadrant I (both positive).
What is the equation of the line in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Equation of the line for the given graph in slope-intercept form is given by y = 5x -1.
As given in the question,
From the given graph,
Consider pair of two coordinates we have,
(x₁ , y₁) = (1, 4)
(x₂ , y₂) = (0,-1)
Equation of the line for the given graph in slope-intercept form is given by:
(y -y₁) / (x -x₁)= (y₂ -y₁) / (x₂ -x₁)
⇒ ( y - 4)/ (x -1) = (-1-4)/(0-1)
⇒(y-4)/(x-1) = 5
⇒y-4 = 5(x-1)
⇒y = 5x -5 +4
⇒ y= 5x -1
Therefore, equation of the line for the given graph in slope-intercept form is given by y = 5x -1.
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Based on the scatterplot, which statements are true? Select TWO correct answers. The kitten should weigh between 22 oz and 24 oz on Day 24. The kitten should have weighed between 5 oz and 7 oz on Day 4. The kitten should have weighed between 7 oz and 9 oz on Day 8. The kitten should have weighed between 13 oz and 15 oz on Day 12. The kitten should have weighed between 12 oz and 14 oz on Day 19.
HELP ASAP!!
The correct statements regarding the scatter plot are given as follows:
The kitten should have weighed between 5 oz and 7 oz on Day 4.The kitten should have weighed between 7 oz and 9 oz on Day 8.For what the scatter plot is used?The scatter plot is used to give the points needed to build the linear regression equation relating the output variable of the vertical axis as a function of the input variable represented by the horizontal axis.
In the context of this problem, these points are given as follows:
(0, 4), (2, 5), (7,7), (9, 10), (14, 12), (15, 15), (21, 17).
Inserting these points into a linear regression calculator, the equation is listed as follows:
y = 0.6529x + 3.65758
On each day listed on the options, the predicted weights are given as follows:
Day 4: 0.6529(4) + 3.65758 = 6.7 oz.Day 8: 0.6529(8) + 3.65758 = 8.9 oz.Day 12: 0.6529(12) + 3.65758 = 11.5 oz.Day 19: 0.6529(19) + 3.65758 = 16 oz.Day 24: 0.6529(24) + 3.65758 = 19.3 oz.From these numeric values, the correct options are selected.
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17 ÷ 2578
Please help I need an answerrrr
Answer: 17/2578 (Decimal: 0.006594)
Step-by-step explanation:
That's the answer :)
What are the coordinates of the vertices after a rotation 90 counterclockwise around the origin.
Answer:When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.
Step-by-step explanation: trust me
Question 5 (5 points)
Find the equation of the line passing through the point (-1, 5) and perpendicular to
the line y=-3x+4.
A) 3y=-x+16
B) 3y=x+16
OC) y=-3x+8
D) y=-3x+2
OLD
Answer:
Option B is perpendicular to y=-3x+4 and goes through point (-1,5)
Step-by-step explanation:
We will look for an equation of the form y=mx+b, where m is the slope and b the y-intercept. The reference line, y=-3x+4, has a slope of -3. A line perpendicular to this line will have a slope that is the "negative inverse" of the refence lines slope. In this case, it's slope would be +(1/3).
We could graph each of the equation options and look for one that is perpendicular, but it might be faster to simply rearrnaged the options into standard format of y=mx+b. which we'll do here:
Option Rearranged Equation Slope
A) 3y=-x+16
y = -(1/3)x+(16/3) -(1/3)
B) 3y=x+16
y = (1/3)x + (16/3) (1/3)
C) y=-3x+8 -3
D) y=-3x+2 -3
There is only one option that has the required slope to be parallel to the reference equation (y=-3x+4), option B: y = (1/3)x + (16/3)
Does it go through point (-1,5)?
y = (1/3)x + (16/3)
Enter x = -1 and find 5:
y = (1/3)(-1) + (16/3)
y = (16/3)-(1/3)
y = (15/3) or 5
Yes, it goes through point (-1,5)
Option B is perpendicular to y=-3x+4 and goes through point (-1,5).
How can the dimensions of algebra tile rectangles and area models be used to represent expressions and multiplication?
The dimensions of algebra tile rectangles and area models can be used to represent expressions and multiplication by measuring the length and breadth of the tiles and multiplying them.
What is a Rectangle?This is referred to as a quadrilateral which has four right angles and the area is calculated by multiplying the length with the breadth.
In as situation where the algebra tile rectangles is used , it is best to first measure the length and the breadth after which they are then multiplied to give the appropriate answer. For example if the length is 8cm and the breadth is 5cm then the area will be 8cm × 5cm = 40cm²
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I need help
There are only 7 blue pens, 4 green pens and 6 red pens in a box
One pen is taken at random from the box
Write down the probability that the pen is blue
Answer: 41.18% or 7/17
Step-by-step explanation:
7 + 4 + 6 = 17
7/17 (fraction)
41.18%
If J is the centroid of CDE, DE = 52, FC = 15,
and HE = 14, find each missing measure.
The measure of missing line segments will be:
DG = 26; GE = 26; DF = 15; CH = 14; CE = 28
What is centroid?The centroid of a triangle is the place where the three medians of the triangle connect. It is sometimes defined as the point at where the three medians cross. A median line connects the middle of a side to the opposing vertex of a triangle. The centroid of a triangle is the point at where the triangle's three medians coincide (each median connecting a vertex with the midpoint of the opposite side).
Here,
IF If J is the centroid of CDE, this means that J divides CG, FE, DC, CE and DH into two equal parts.
The following expressions are therefore true
DG + GE = DE and DG = GE
Substituting
DG + DG = DE
2DG = DE
Given DE = 52
2DG = 52
DG = 52/2
DG = 26
Since DG = GE, hence GE = 26
Also DF + FC = DC and DF = FC
Since FC = 15, hence DF = 15
Also CH + HE = CE and CH = HE
Since HE = 14, hence CH = 14
CE = 14+14
CE = 28
The missing line segment count will be: DG = 26; GE = 26; DF = 15; CH = 14; CE = 28.
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Brian loves to bake blueberry muffins for his friends and family.
there is a proportional relationship between the volume of flour brian uses (in cups), x, and
the number of muffins he bakes, y.
10
9
8
7
9
s
s
3
2
2
s
9
00
9
10
For a proportional relationship between the volume of flour used (in cups), x, and the number of baked muffins, y, the constant of proportionality is 4.
Constant of proportionality, also known as constant ratio or constant rate, refers to is the ratio that relates two given values in a data set that is represented as a proportional relationship. When two parameters are proportional, either directly or indirectly, the relationship is expressed as a = kb or a = k/b, where k indicates the relationship between the two variables and is known as the proportionality constant. In the given data, the proportionality constant is:
k =b/a = 8/2 =12/3 = 16/4 = 20/4 = 4
Hence, the proportionality constant for the given data is 4.
Notes: The question is incomplete. The complete question is: Brian loves to bake blueberry muffins for his friends and family. There is a proportional relationship between the volume of flour brian uses (in cups), x, and the number of muffins he bakes, y. What is the constant of proportionality. (Refer to the table).
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An astronaut has an annual income of $161,141.00.
The income tax an astronaut must pay is 8%.
What is the amount of income tax in dollars and cents that the
astronaut must pay?
yesterday, Austin burned 199 calories while exercising. Today, he burned 1008.8 calories. How many more calories did Austin burn today than yesterday?
Answer: Austin burn 809.8 more calories today than yesterday.
G(F(x)) = (x - 5)3 + x - 5
A.
F(x) = x - 5 and G(x) = (x - 5)3
B.
F(x) = x - 5 and G(x) = x3 + x
C.
F(x) = (x - 5)3 and G(x) = x - 5
D.
F(x) = x3 + x - 5 and G(x) = x - 5
Option B is correct.
Given that Function G(F(x)) = (x - 5)3 + x - 5 ;
Lets take a function G(x) = x3 + x as (i) and check that it will produce the above equation or not.
Now suppose that the value of the function F(x) = x-5 as (ii) , using this value we will check that whether it support the value for g(x) or not.
Put the value of function f(x) in the equation number i , it will be like this :
G(f(x)) = f(x)3 + f(x)
we know that the value of f(x) from (ii)
Therefore, G(f(x)) will be :
G(f(x)) = (x - 5)3 + x - 5, this will satisfy the above equation which means our supposition was correct. Hence the correct ans is B
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Isosceles Trapezoids in Summary
Check ALL of the statements that are ALWAYS true about ISOSCELES TRAPEZOIDS.
(Select all that apply.)
1. SIDES: One pair of opposite sides are parallel.
2. SIDES: One pair of opposite sides are congruent.
3. SIDES: A pair of adjacent sides are congruent.
4. ANGLES: Sum of the angles is 360°.
5. ANGLES: One set of opposite angles are congruent.
6. ANGLES: Consecutive angles are congruent.
7. ANGLES: All four angles are right angles.
8. ANGLES: Consecutive angles are supplementary.
9. DIAGONALS: One of the diagonals bisects the other.
10. DIAGONALS: Diagonals are congruent.
11. DIAGONALS: Diagonals intersect perpendicularly.
12. DIAGONALS: Diagonals bisect a pair of vertex angles of the shape.
The statements that are always true about Isosceles Trapezoids:
One pair of opposite sides are parallel.
One pair of opposite sides are congruent.
The sum of the angles is 360°.
Diagonals are congruent.
Diagonals intersect perpendicularly.
What is an isosceles trapezoids?
A convex quadrilateral having one pair of opposite sides divided by a line of symmetry is known as an isosceles trapezoid. It is a particular instance of a trapezoid. Alternately, it can be described as a trapezoid whose base angles and both legs are identical in size.
The true statements are:
One pair of opposite sides are parallel.
One pair of opposite sides are congruent.
The sum of the angles is 360°.
Diagonals are congruent.
Diagonals intersect perpendicularly.
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14x²y – 21xy² + 28x²y²
Answer:
7xy(2x-3y+4xy)
Step-by-step explanation:
14÷7=2
21÷7=3
28÷7=4
they all have 7, x and y so that would be on the outside
help meeeeeeeeeeeeeee pleaseee
Answer:
You have to place the numbers given or your left in the formula given. So for example: y= 2*(-2)^2
that's: y=2*4, so: y=8
1) y=8
2) y= 2*(-1)^2. y=2
3) y= 2*(0)^2. y=0
4) y= 2*(1)^2. y=2
5) y= 2*(2)^2. y=8
the ph measurements of water specimens from various locations along a given river basin are normally distributed with mean 8 and standard deviation 0.3. what is the approximate probability that the ph measurement of a randomly selected water specimen is greater than 8.2? 0.7475 0.2525 0.7525 0.2475
0.7475 is the approximate probability that the ph measurement of a randomly selected water specimen is greater than 8.2
P( A ≥ 8.2) = P( (Z ≥ 8.2 − 8)/0.3)
= P(Z ≥0.66)
= 0.7475
normsdist(0.666666) =0.7475
The standard normal cumulative distribution function is returned. The mean of the distribution is 0 (zero), while the standard deviation is one. Instead of a table of standard normal curve areas, use this function.The concentration of hydronium (H3O+) ions in an aqueous solution is measured by pH. It is measured from 0 to 14 on a negative logarithmic scale.
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III. Write each quadratic equation in standard form
1. 3x-2x² = 7
2.5-2x² = 6x
3.(x+3)(x+4)=0
4.(2x + 7)(x-1)=0
5,2x(x-3) = 15
ax²+bx+c=0
Answers are attached
Write your answers hhere
Answer:
Step-by-step explanation:
The answer is 6.
I got this by subtracting 23 by 12 (the number of numbers shown). Then I got 11. So I followed the pattern until I got six.
23-12=11
2,4,6,8,2,4,6,8,2,4,6,8,......2,4,6,8,2,4,6,8,2,4,6
Christian buys 18 bottles of grapefruit juice at the corner store for a total cost of $15.66. If each bottle costs the same amount, how much is 3 bottles of juice?
Answer:$2.61
Step-by-step explanation:
18=$15.66
÷6 ÷6
3=$2.61
The cost of 3 bottles of juice based on the given ratio will be $2.61.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
18 bottles cost = $15.66
1 bottle cost = $15.66/18 = $0.87/ bottle
For 3 bottles = 3 × $0.87 = $2.61
Hence "The cost of 3 bottles of juice based on the given ratio will be $2.61".
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Jeanne has 3 7/8 yards of fabric. The table shows the amount of fabric she needs for different items. How many pairs of shorts can she make?
Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric.
What do you mean by ratio?
The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Given that,
The total amount of fabric = 3 7/8 yards = 31/8 yards.
Amount of fabric needed to make 1 pair of shorts = 1 1/4 = 5/4 yards.
The number of shorts that can be made = 31/8 ÷ 5/4
⇒ 3.1 so it will be 3 because no relevance of decimal shorts.
Hence "Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric".
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What is the slope of the line that passes through the points (-5,2) and (-1,-6)
Answer:
Slope = -2
Step-by-step explanation:
Slope of Line passes through two Points [tex](x_{1},y_{1} )[/tex] and [tex](x_{2},y_{2} )[/tex]
is given by [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
So by Substitution
[tex]m=\frac{-6- 2 }{-1 - (-5)}=\frac{-8}{4} =-2[/tex]
The ratios in an equivalent ratio table are 3:12, 4:16, and 5:20. If the first number in the ratio is 10, what is the second number? Justify your reasoning
.
Answer:
40
Step-by-step explanation:
Looking at the other examples, its shows the the second number is always 4 times bigger/ahead then/of the first number.