Answer:
see below
Step-by-step explanation:
Let g= amount that gail has
j = g+10
j+g ≤ 27
Substitute the first equation into the inequality
g+g+10 ≤ 27
2g + 10 ≤ 27
Subtract 10 from each side
2g≤ 17
Divide by 2
g≤ 8.5
Answer:
Let g= amount that gail has
j = g+10
j+g ≤ 27
Substitute the first equation into the inequality
g+g+10 ≤ 27
2g + 10 ≤ 27
Subtract 10 from each side
2g≤ 17
Divide by 2
g≤ 8.5
Step-by-step explanation:
Can you answer the question
Answer:
Um c
Step-by-step explanation:
suppose y varies directly as x, and y=48 when x=6. find x when y=72.
Using the constant of proportionality the value of x when y is 72 is 9.
What is a COP?
The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.
If y varies directly as x, it means that y can be expressed as a constant multiple of x, i.e., y = kx, where k is the constant of proportionality.
To find k, we can use the given information that y = 48 when x = 6 -
y = kx
48 = k(6)
k = 8
Now that we know k, we can use it to find x when y = 72 -
y = kx
72 = 8x
x = 9
Therefore, when x = 72, the value of x = 9.
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Consider a particular baseball player at bat. The height of the ball at time t can be modeled by h=-16t^2+v t+h. Here, v is the initial upward velocity of the ball, and h is the height at which the ball is hit. if a ball is 4 feet off the ground when it is hit with a negligible upward velocity close to 0 feet per second, when will the ball hit the ground?
Solve for \(t\) when \(h=0\), given \(v_0=0\) and \(h_0 = 4\).
\(0 = -16t^2 + 4 \implies 16t^2 = 4 \implies t^2 = \dfrac14 \implies t = \dfrac12\)
so it will take half a second for the ball to hit the ground.
Which cause do you think was the most important of the Great Depression why?
Answer:
The stock market crash of 1929 touched off a chain of events that plunged the United States into its longest, deepest economic crisis of its history. It is far too simplistic to view the stock market crash as the single cause of the Great Depression. A healthy economy can recover from such a contraction.
Step-by-step explanation:
A rectangle is 1/2 feet long and 3/4 feet wide.
What is the area of the rectangle?
Enter your answer as a fraction in simplest form
Answer: 3/8
Step-by-step explanation: All you do is 1/2 times 3/4. Numerator times numerator. The Denominator times denominator.
Numerators first- 1x3Denominators second 2x4
(x + 3) metres
(2x - 1)metres
The area of triangle ABC is 6√2 m².
Calculate the value of x.
Give your answer correct to 3 significant figures.
Answer: 2.63
Step-by-step explanation:
Using the formula \(A=\frac{1}{2} ab \sin C\),
\(6\sqrt{2}=\frac{1}{2}(2x-1)(x+3) \sin 45^{\circ}\\\\6\sqrt{2}=\frac{(2x-1)(x+3)}{2} \cdot \frac{\sqrt{2}}{2}\\\\6=\frac{(2x-1)(x+3)}{4}\\\\24=(2x-1)(x+3)\\\\24=2x^2 +5x-3\\\\2x^2 +5x-27=0\\\\x=\frac{-5 +\sqrt{5^2 -4(2)(27)}}{2(2)} \text{ } (x > 0)\\\\x=\frac{\sqrt{241}-5}{4} \approx 2.63\)
The final exam grade distribution for all students in the introductory statistics class at a local community college is displayed in the table, with A = 4, B = 3, C = 2, D = 1, and F = 0. Let X represent the grade for a randomly selected student from the class. A 2-column table with 5 rows. Column 1 is labeled grade with entries 4, 3, 2, 1, 0. Column 2 is labeled probability with entries 0.4, 0.32, 0.17, 0.08, 0.03. What is the mean of the distribution? 2 3 2.98 3.50
The mean of the discrete distribution that models this situation is of 2.98.
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
Considering the table, the probability distribution is given by:
P(X = 4) = 0.4.P(X = 3) = 0.32.P(X = 2) = 0.17.P(X = 1) = 0.08.P(X = 0) = 0.03.Hence the mean is given by:
E(X) = 4 x 0.4 + 3 x 0.32 + 2 x 0.17 + 1 x 0.08 + 0 x 0.03 = 2.98.
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Find the power of 9↑1. Type your answer using digits.
Answer:
9^1 has a power of 1. it evaluates to 9
Step-by-step explanation:
The lengths of two sides of the right triangle ABC shown in the illustration givena=12 cm and c= 20cm
In the right triangle of sides a, b, and c
\(a^2+b^2=c^2\)Since a = 12 and c = 20
Substitute them in the given rule
\(\begin{gathered} (12)^2+b^2=(20)^2 \\ 144+b^2=400 \end{gathered}\)Subtract 144 from both sides
\(\begin{gathered} 144-144+b^2=400-144 \\ b^2=256 \end{gathered}\)Take a square root for both sides
\(\begin{gathered} \sqrt[]{b^2}=\sqrt[]{256} \\ b=16 \end{gathered}\)The answer is b = 16
In a recent year, a university had an enrollment of 15,363 male and 19,512 female undergraduate students. The total number of full-time instructional faculty was 1,849. Find the ratio of students to full-time instructional faculty as a unit ratio. Round to the nearest whole number.
The required ratio of students to teachers is 19: 1.
Given that,
The total enrollment of male students and female students is 15,363 male and 19,512 female respectively.
The total number of full-time instructional faculty was 1,849.
To determine the ratio of students to teachers.
Here,
Total students = 15363 + 19512 = 34875
Number of teachers = 1849
Now,
Ratio = total students / teacher
Ratio = 34875 / 1849
Ratio = 19 : 1
Thus, the required ratio of students to teachers is 19 : 1.
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The back of Dante's property is a creek. Dante would like to enclose a rectangular area, using the creek as one side and fencing for the other three sides, to create a pasture. If there is 960 feet of fencing available, what is the maximum possible area of the pasture?
Answer:
Step-by-step explanation:
960/3. that's 320 a side. They said maximum, I'm guessing they just wanted you to use base times height as if it was a square, since I'm not seeing any other information. the maximum possible area would be, if the sides were 320 each would be 102,400 square feet. Maximum
What would be x please help me
Answer:
\(18.83\)
Step-by-step explanation:
For right triangles only, the tangent of an angle is equal to its opposite side divided by its adjacent side.
Therefore, we have the equation:
\(\tan 33^{\circ}=\frac{x}{29},\\x=29\tan 33^{\circ}\approx \boxed{18.83}\)
6h+(−8.1d)−14+5d−2.5h
Answer:
3.5h-3.1d-14
Step-by-step explanation:
6h+(−8.1d)−14+5d−2.5h
Combine like terms
6h -2.5h -8.1d +5d -14
3.5h-3.1d-14
Please help me with this.
Here are the correct matches to the expressions to their solutions.
The GCF of 28 and 60 is 4.
(-3/8)+(-5/8) = -4/4 = -1.
-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.
The solution of 0.5 x = -1 is x = -2.
The solution of 1/2 m = 0 is m = 0.
-4 + 5/3 = -11/3.
-2 1/3 - 4 2/3 = -10/3.
4 is not a solution of -4 < x.
1. The GCF of 28 and 60 is 4.
The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:
28 = 2 x 2 x 7
60 = 2 x 2 x 3 x 5
The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.
2. (-3/8)+(-5/8) = -1.
To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.
3. -1/6 DIVIDED BY 1/2 = -1/3.
To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.
4. The solution of 0.5 x = -1 is x = -2.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.
5. The solution of 1 m = 0 is m = 0.
To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.
6. -4 + 5/3 = -11/3.
To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.
7. -2 1/3 - 4 2/3 = -10/3.
To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.
8. 4 is not a solution of -4 < x.
The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.
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A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.
The area of the shaded region is equal to 45 square units.
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LW
Where:
A represent the area of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the area of a rectangle, we have the following;
Area of rectangle = 8 × 6
Area of rectangle = 48 square units.
Since the opposite sides of any rectangle are congruent (equal), the legs of the right triangle can be calculated as follows;
L₁ = 8 - 5 = 3 units.
L₂ = 6 - 4 = 2 units.
Area of right triangle = 1/2 × 3 × 2
Area of right triangle = 3 square units.
For the area of the shaded region, we have:
Area of the shaded region = 48 square units - 3 square units.
Area of the shaded region = 45 square units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
HELP A FRIEND IN NEED
Answer:
Angle A = 68 degree
Angle B = 44 degree
Step-by-step explanation:
Sum of all interior angles = Angle A+Angle B+ Angle C
180 = 68+x+x-24
180 = 68+2x-24
180-68 = 2x-24
112+24 = 2x
136/2 = x
68 = x
Therfore, Angle A = 68 degree
Angle B = (x-24)
= (68-24)
= 44 degree
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Which of the following numbers is rational? Assume that the decimal patterns continue.
9514 1404 393
Answer:
(c) √49
(d) 2.544544...(3-digit repeat)
Step-by-step explanation:
Square roots of perfect squares are rational, as are repeating decimals.
Of the following three statements, choose the best option and write a viable argument showing how it is reflected by the Cost Function for Wichita’s factory.
___ The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.
___ The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.
___ Overtime wages were required to produce at levels above 25,000 units.
The cost per unit actually comes down to 0.8$per unit.
We have given that,
The electricity contract with the utility company is structured so that higher daily energy usage is charged at a lower rate.
The plant’s production processes are performed primarily by robots that are able to work longer hours, when needed, at no additional cost.
Overtime wages were required to produce at levels above 25,000 units.
What is the cost?
A cost is an expenditure required to produce or sell a product or get an asset ready for normal use.
The cost of production per unit of the item produced is 1$ as long as the total units produced are less than 2500.
If more than 2500 units are produced then the cost per unit actually comes down to 0.8$per unit.
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Let v represent the value of a bank acount, in thousands of dollars, t yearsaftertye account is opend at the bank
Answer:
could you explain it more
Step-by-step explanation:
Collect data on the OBSERVATION table in ANNEXURE A to record 30 days of the minimum and maximum temperature in your community. Arrange the maximum temperature of the 30 days in ascending order to summarize the data. Determine the mean, mode, median, and range. Use the maximum temperature data and draw for each section a frequency table with appropriate intervals in ANNEXTURE B Display or represent the data from the frequency table on a pie chart in ANNEXTURE B. First, calculate the size of the angles for the pie chart. Example: Intervals between 20-30 are 5. Therefore the proportion of the Segment: 11 [360° = 72° Show all your calculations. 11 Which data collection best describe the maximum and why?
Answer:
I do not have access to Annexure A and Annexure B, so I cannot collect the data, draw the frequency table or pie chart, or answer the last question. However, I can provide a general explanation of how to calculate the mean, mode, median, and range from a set of data.
To find the mean (average) of a set of data, add up all the values in the set and divide by the number of values. For example, if the maximum temperatures of the 30 days are:
25, 28, 29, 27, 26, 30, 31, 32, 29, 27, 26, 24, 23, 25, 28, 30, 32, 33, 34, 31, 29, 28, 27, 26, 25, 24, 23, 21, 20, 22
The sum of the values is:
25 + 28 + 29 + 27 + 26 + 30 + 31 + 32 + 29 + 27 + 26 + 24 + 23 + 25 + 28 + 30 + 32 + 33 + 34 + 31 + 29 + 28 + 27 + 26 + 25 + 24 + 23 + 21 + 20 + 22 = 813
Dividing by the number of values (30), we get:
Mean = 813/30 = 27.1
To find the mode of a set of data, identify the value that occurs most frequently. In this example, there are two values that occur most frequently, 27 and 29, so the data has two modes.
To find the median of a set of data, arrange the values in order from smallest to largest and find the middle value. If there are an even number of values, take the mean of the two middle values. In this example, the values in ascending order are:
20, 21, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 27, 27, 28, 28, 29, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34
There are 30 values, so the median is the 15th value, which is 28.
To find the range of a set of data, subtract the smallest value from the largest value. In this example, the smallest value is 20 and the largest value is 34, so the range is:
Range = 34 - 20 = 14
To create a frequency table for the maximum temperature data, we need to group the data into intervals and count the number of values that fall into each interval. For example, we could use the following intervals:
20-24, 25-29, 30-34
The frequency table would look like this:
Interval | Frequency
20-24 | 4
25-29 | 18
30-34 | 8
To calculate the size of the angles for the pie chart, we need to find the total frequency (30) and divide 360° by the total frequency to get the proportion of each interval in degrees. For example, for the interval 25-29:
Proportion = Frequency/Total frequency = 18/30 = 0.6
Angle = Proportion * 360° = 0.6 * 360° = 216°
We can repeat this calculation for each interval to obtain the angles for the pie chart.
In terms of the last question, it is not clear what is meant by "which data collection best describe the maximum and why?". If you could provide more context or clarification, I would be happy to try to help.
Question 4Mple Choice Worth 2 points)
Ares of Polygons and Composite Figures MC)
A composte figure is shown
024413
028.445²
1.15 in
Which of the following represents the total area of the figure?
010 663 ²
034.335 ²
4.6 in.
3h 563
P
The total area of the composite figure which has triangle and rectangle is 24.41 square inches
The given composite figure has two triangles and one rectangle
Area of rectangle =length × width
=4.6×3.15
=14.49 square inches
Area of left side triangle, it has base of 3.3 in and height 3.15 inches
Area of triangle = 1/2×3.3×3.15
=5.1975 square inches
Area of triangle on right side
Base = 3 in
Height = 6.3-3.15=3.15 in
Area of triangle = 1/2×3×3.15
=4.725 square inches
Total area = 14.49 + 5.1975 + 4.725
=24.41 square inches
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Which expression is equivalent to 9(4+2x)?
Shown below is a wooden six-sided (hexagon) frame. Which of
the following best approximates the slopes of the six line
segments?
O The slopes are approximately -1.4, 0, and 1.4.
O The slopes are approximately -1.7, 0, and 1.7.
O The slopes are approximately -1.8, 1, and 1.4.
O The slopes are approximately -1.7,0, and 1.4
The slopes are best approximated as: The slopes are approximately -1.7, 0, and 1.7.
How to find the slope between two coordinates?The formula to find the slope between two coordinates is expressed as:
Slope = (y₂ - y₁)/(x₂ - x₁)
The slope of each line above the x-axis are:
Slope 1 = (5 - 0)/(5 - 8)
Slope 1 = -1.7
Slope 2 = (5 - 5)/(5 - (-2))
Slope 2 = 0
Slope 3 = (5 - 0)/(-2 - (-5))
Slope 3 = 5/3 = 1.7
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What is F(-x)?
F(x)=x^3+1
Answer:
F(-x) = 0
Step-by-step explanation:
What is F(-x)?
F(-x) = F(-1)
F(x) = x³ + 1 F(-1)
F(-1) = -1³ + 1
F(-1) = -1 + 1
F(-1) = 0
So, F(-x) = 0
Answer:
f(-1) = 0
Step-by-step explanation:
Evaluating a function for f(-x) is the same as evaluating it for f(-1).
So we plug in -1 instead.
f(-1) = x³ + 1
= (-1)³ + 1 (here we cube -1)
= -1 + 1 (here we subtract)
= 0 (and, this is the answer)
\(\therefore\) The answer is f(-1) = 0
A manager drew this box-and-whisker plot to represent the ages of the company’s 240 employees. How many employees are younger than 42?
24
48
60
75
Answer:
its 60, need proof?
Step-by-step explanation:
Answer: 60
Step-by-step explanation: I took the test and got it right. Goodluck with the rest!
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
simplify 5(x - y) - (x - y)
Answer:
4(x - y)
Step-by-step explanation:
5(x - y) - (x - y) - Distribution the numbers outside the brackets (There is a neg one in front of the second (x - y)
5x - 5y - x + y - Simplify
4x - 4y
4(x - y) - Optional
Triangle ABC was dilated using the rule DO,4. Triangle A'B'C' is the result of the dilation.
Point O is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of O B is three-fourths.
What is OB'?
1.5 units
3 units
4.5 units
6 units
Mark this and return
Answer:
(b) 3 units
Step-by-step explanation:
You want to know the length of OB' when OB = 3/4 and ∆ABC is dilated about point O by a factor of 4.
DilationThe dilation factor multiplies every length.
If OB is 3/4, then OB' is 4(3/4) = 3.
The length of OB' is 3 units.
<95141404393>
choose the general algebraic representation (notation) for transforming pentagon vwxyz into pentagon qrstu.
The transformation function can be represented as vwxyz \($\rightarrow$\)qrstu = (v,w,x,y,z) \($\rightarrow$\) (q,r,s,t,u).
This algebraic representation of the transformation of pentagon vwxyz into pentagon qrstu is using the notation of a function. A function takes an input (in this case, the coordinates of pentagon vwxyz) and produces an output (in this case, the coordinates of pentagon qrstu). This transformation can be represented by the notation (v,w,x,y,z) \($\rightarrow$\) (q,r,s,t,u). This notation means that the coordinates (v,w,x,y,z) are being transformed into the coordinates (q,r,s,t,u). This notation is a concise way of expressing the transformation of pentagon vwxyz into pentagon qrstu. It is important to note that the transformation itself is not specified; the notation is simply used as a way of representing the transformation.
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a is directly proportional to b. When a is 6, b is 72. Find b when a is 8. 3
Answer:
a) "K" is proportional Constant K= 0.0833
b) The value of b = 99.639
Step-by-step explanation:
Explanation :-
Given 'a' is directly proportional to 'b'
a ∝ b
a = k b ....(i)
where "K" is proportional Constant
Case(i):-
when a =6 and b=72
a = k b
⇒ 6 = k (72)
⇒ \(K = \frac{6}{72} = \frac{1}{12} = 0.0833\)
Case(ii):-
Given a = 8.3
a = k b
⇒ 8.3 = 0.0833 ×b
⇒ \(b = \frac{8.3}{0.0833} = 99.639\)
Final answer:-
a)"K" is proportional Constant K= 0.0833
b) The value of b = 99.639