Answer:
a) Prepare a frequency table for the data
Step-by-step explanation:
Are the equations 5x=24+2x and 3x=24 equivalent?
Answer:
Yes they are.
Step-by-step explanation:
By simply moving 2x from the LHS to the RHS we'll get it's equivalent to be 3x.
i.e 5x - 2x = 3x
Sketch the graph of y = negative 2 x squared + x + 1 using your graphing calculator. What are the x-intercepts of this graph? a. (1, 0) and (-0.5, 0) c. There are no x-intercepts b. (-2.5, 0) and (-2, 0) d. (-1.5, 0) and (-0.5, 0)
The x-intercept is (1, 0) and (-0.5, 0).
The correct option is (a)
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
Given function is:
f(x)= [tex]-2x^{2}+x+1[/tex]
So, The graph of this equation is attaches below.
The x- intercepts of this graph
[tex]\mathrm{X\:Intercepts}:\:\left(-\frac{1}{2},\:0\right),\:\left(1,\:0\right)[/tex]
or
X intercepts: (1, 0) and (-0.5, 0)
Hence, the x-intercept is (1, 0) and (-0.5, 0).
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find the angle of elevation of the sun if a building 325 feet tall casts a shadow 296 feet long
Answer:
Step-by-step explanation:
SOH CAH TOA
we have the (opposite) --> 325
we have the (adjacent) --> 296
so do the inverse tan of opposite over adjacent...
[tex]tan^{-1} (\frac{325}{296} ) = 47.67[/tex] degrees
the prom committee is made up of 8 boys and girls. If there are 12 boys and 15 girls in the group to pick the committee from, how many ways can the committee be organized?
1). 1860 ways
2). 3185325 ways
3). 2220075 ways
4). 675675 ways
Thanks guys!!
The number of ways can the committee be organized will be 2220075. Then the correct option is 3.
What are permutation and combination?A permutation is an act of putting things or elements in the right sequence. Combinations are a method of picking things or pieces from a collection of objects or sets when the sequence of the objects is irrelevant.
The prom committee is made up of 8 boys and girls.
If there are 12 boys and 15 girls in the group to pick the committee from.
Then the number of ways can the committee be organized will be
Then the number of ways is given by the combination formula. Then we have
Number of ways = ¹²C₀ x ¹⁵C₈ + ¹²C₁ x ¹⁵C₇ + ¹²C₂ x ¹⁵C₆ + ¹²C₃ x ¹⁵C₅ + ¹²C₄ x ¹⁵C₄ + ¹²C₅ x ¹⁵C₃ + ¹²C₆ x ¹⁵C₂ + ¹²C₇ x ¹⁵C₁ +¹²C₈ x ¹⁵C₀
Number of ways = 6435 + 77220 + 330330 + 660660 + 675675 + 360360 + 97020 + 11880 + 495
Number of ways = 2220075
Thus, the correct option is 3.
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The area A of a circle is the product of π and the radius r squared
i need written in a algebraic equation
Answer:
A=πr^2
Step-by-step explanation:
A=π*r^2
Where, A is area of circle
r is radius of circle
π is constant
.
Hope it's help and I think I have give brainleist answer
Answer:
πr^2
Step-by-step explanation:
it's just πr^2.
easy
For his phone service, Chris pays a monthly fee of $25, and he pays an additional $0.06 per minute of use. The least he has been charged in a month is $86.74.
What are the possible numbers of minutes he has used his phone in a month?
Use M for the number of minutes, and solve your inequality for M.
Answer:
1029 minutes or 17.15 hours
Step-by-step explanation:
25+0.06M=86.74
0.06M=61.74
M=61.74/0.06=1029
what is the solution to the inequality below 14-2(x+1)< -4
Answer:
x > 8
Step-by-step explanation:
14 - 2(x + 1) < - 4 ← distribute parenthesis and simplify left side
14 - 2x - 2 < - 4
12 - 2x < - 4 ( subtract 12 from both sides )
- 2x < - 16
divide both sides by - 2 , reversing the symbol as a result of dividing by a negative quantity.
x > 8
Which is the standard form of the equation of a parabola with a focus of (8, 0) and directrix x = –8?
Answer:
Hi,
Step-by-step explanation:
directrix: x=-8
focus=(8,0)
[tex]x=\dfrac{(y-0)^2}{2*(8+8)}+\dfrac{8-8}{2}\\\\\boxed{x=\dfrac{y^2}{32}}[/tex]
Sam borrowed $2,000,000 for a
period of four years. his interest
rate is 5%. how much interest will
sam pay in all?
helpp
The total amount Sam will pay in all will be $2,400,000
Simple interest
From the question, we are to determine the interest Sam pays in all
Using the simple interest formula,
I = PRT
From the given information,
P = $2,000,000
R = 5% = 0.05
T = 4
Putting the parameters into the formula,
I = $2000000 × 0.05 × 4
I = $400000
The interest Sam will pay is $400,000
The total amount Sam will pay in all will be $2,000,000 + $400,000
= $2,400,000
Hence, the total amount Sam will pay in all will be $2,400,000
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Answer:
Step-by-step explanation:400000
A map shows that the vertices of a backyard are W(-100,-70), X(-100,0),Y(0,0), and Z(-60,-70) . The coordinates are measured in feet. The line segment XZ separates the backyard into a lawn and a garden. The area of the lawn is greater than the area of the garden. How many times larger is the lawn than the garden?
The area of the lawn is 2.5 times greater than the area of the garden.
What is Heron's formula in math?Heron's formula for finding the area of a triangle in terms of the lengths of its sides.
In symbols, if a, b, and c are the lengths of the sides: Area = √s(s - a)(s - b)(s - c) where s is half the perimeter, or (a + b + c)/2.
Given vertices W(-100,-70), X(-100,0),Y(0,0), and Z(-60,-70) of a backyard,
We have to find distances WX, XY, YZ, ZW and XZ:
1. WX= √(-100+100)²+(0+70)²
=√0+4900
=70
2. XY= √(0+100)²+(0-0)²
=100 units.
3. YZ= √(-60-0)²+(-70-0)²
=√3600+4900
= √8500= 10√85
4. ZW= √(-60+100)²+(-70+70)²
=√40²+0
=40 units
5. XZ= √(-60+100)²+(-70+0)²
=√40²+70²
=√6500=10√65
Then:
1. the area of WXZ
[tex]\sqrt{(70+40+10\sqrt{65}) /2 * ({70+40+10\sqrt{65}) /2 -70* {(70+40+10\sqrt{65}) /2 -40[/tex]*[tex]\sqrt{(70+40+10\sqrt{65}) /2 -10\sqrt{65}[/tex]
=1400 feet²
Area of XYZ= [tex]\sqrt{(100+10\sqrt{65}+10\sqrt{85}) /2 * (100+10\sqrt{65}+10\sqrt{85}) /2 -100* {(100+10\sqrt{85}+10\sqrt{65}) /2[/tex]-[tex]\sqrt{-10\sqrt{85}*(10+10\sqrt{85} +10\sqrt{65}) /2 -10\sqrt{65}[/tex]
=3500 feet²
Then, ar(WXZ)/ ar (XYZ)= 3500/1400=2.5 times.
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how to find the volume of a room
multiply the height x the length x the width to find the volume of a room (or another 3d object)
There are 4 quarters, 5 nickels and 3 dimes in a jar. One coin is randomly drawn,
replaced and then another coin is drawn.
What is the probability of getting a quarter then a nickel?
5/36
9/12
9/144
1/5
Answer:
[tex]\displaystyle\frac{5}{36}[/tex]
Step-by-step explanation:
Probability is used to find how likely an outcome is to happen. Probability can be expressed as a fraction with the total outcomes as the denominator and the number of successful outcomes (what you want to happen) as the numerator.
Sample Size
The sample size is the number of possible outcomes. In this case, the sample size will be the total number of coins. To find the sample size we need to add together all of the coins.
4 + 5 + 3 = 12This means that the sample size is 12. For this type of probability, the sample size will serve as the denominator for each probability.
Replacement
In the question, it is stated that coins are replaced. This means that the sample size will not change at any point. So, the denominator will be the same for every probability.
Creating Probability Fractions
We are looking for the probability of getting a quarter and nickel, so we need to find the fractions that represent both situations.
First, let's find the quarter. As stated in the first paragraph, the number of successful outcomes is the numerator. There are 4 quarters, so 4 is the number of successful outcomes. Therefore, 4 will be the numerator. Then, 12 will be the denominator because 12 is the sample size.
[tex]\displaystyle\frac{4}{12}[/tex]Next, we need to find the probability of a nickel. Since there are 5 nickels, there are 5 successful outcomes. Then, the sample size is still 12 because there is replacement.
[tex]\displaystyle\frac{5}{12}[/tex]Complex Probability
Now we have the probability of both a quarter and nickel alone. However, this question asks about the probability of both, so this is an example of complex probability. To find complex probability, you have to multiply each probability together.
[tex]\displaystyle\frac{4}{12} *\frac{5}{12}=\frac{20}{144}[/tex]To reach the final answer we have to simplify the answer.
[tex]\displaystyle\frac{20}{144} =\frac{5}{36}[/tex]This means that the probability of pulling a quarter and then a nickel is 5/36.
The circumference of the hub cap of a tire is 80.07 centimeters. find the area of this hub cap. use
3.14 for it. if the circumference of the hub cap were smaller, explain how this
would change the area of the hub cap.
the area of this hub cap is about how many
square centimeters?
The area of this hub cap is about 510.44625 cm².
What is Area of Circle?The area of circle is pi times the square of the radius.
Area of circle =π r²
Circumference (C) = 2π r
80.07 = 2 (3.14) r
76.87/ (2x 3.14) =r
r = 12.75 cm
now, Area be
=π r²
= 3.14*12.5*12.75
=510.44625 cm²
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What is the slope of the line graphed below?
(-2,2)
(3, 1)
Answer:
-1/5
Step-by-step explanation:
To find the slope, the formula is y2-y1/x2-x1
1-2/3-(-2) = -1/5
Answer:
‐1/5Step-by-step explanation:
hope this helps!!!!
Solve- x/x+1 - 1/2 = -1/x+1
Answer:
Step-by-step explanation:
Remark
x/(x+1) - 1/2 = -1 /(x + 1) is the equation to be solved. Add 1/(x + 1 to both sides
x/(x+1) + 1/(x+1) - 1/2 = -1/(x + 1) + 1/(x + 1) Combine
x/(x+1) + 1/(x + 1) - 1/2 = 0 Combine x/(x+1) + 1/(x+1)
(x + 1)/(x + 1) - 1/2 = 0 Cancel (x+1)/(x+1) = 1
1 - 1/2 = 0 No solution
Answer: No solution
Evaluate the surface integral ∫sf⋅ ds where f=⟨2x,−3z,3y⟩ and s is the part of the sphere x2 y2 z2=16 in the first octant, with outward normal orientation away from the origin
Parameterize S by the vector function
[tex]\vec s(u,v) = \left\langle 4 \cos(u) \sin(v), 4 \sin(u) \sin(v), 4 \cos(v) \right\rangle[/tex]
with 0 ≤ u ≤ π/2 and 0 ≤ v ≤ π/2.
Compute the outward-pointing normal vector to S :
[tex]\vec n = \dfrac{\partial\vec s}{\partial v} \times \dfrac{\partial \vec s}{\partial u} = \left\langle 16 \cos(u) \sin^2(v), 16 \sin(u) \sin^2(v), 16 \cos(v) \sin(v) \right\rangle[/tex]
The integral of the field over S is then
[tex]\displaystyle \iint_S \vec f \cdot d\vec s = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \vec f(\vec s) \cdot \vec n \, du \, dv[/tex]
[tex]\displaystyle = \int_0^{\frac\pi2} \int_0^{\frac\pi2} \left\langle 8 \cos(u) \sin(v), -12 \cos(v), 12 \sin(u) \sin(v) \right\rangle \cdot \vec n \, du \, dv[/tex]
[tex]\displaystyle = 128 \int_0^{\frac\pi2} \int_0^{\frac\pi2} \cos^2(u) \sin^3(v) \, du \, dv = \boxed{\frac{64\pi}3}[/tex]
100 POINTS PLEAS please help
(-2u3 + 5u - 1) + (7u3 - 2u2 + 9)
A) 5 u3 - 2 u2 + 5 u + 8
B) -5 u3 - 2 u2 + 5 u + 10
C)5 u3 + 3 u + 8
Answer:
[tex]\textsf{A)} \quad 5u^3-2u^2+5u+8[/tex]
Step-by-step explanation:
Given expression:
[tex](-2u^3+5u-1)+(7u^3-2u^2+9)[/tex]
Remove parentheses:
[tex]\implies -2u^3+5u-1+7u^3-2u^2+9[/tex]
Collect like terms:
[tex]\implies -2u^3+7u^3-2u^2+5u-1+9[/tex]
Combine like terms:
[tex]\implies 5u^3-2u^2+5u+8[/tex]
Option A
if a= 2x-3 and b= 2x+5
determine the product of a and b by using formulae. if x=2, ab= what?
help pleasee would appreciate a lot
Answer:
a= 2x-3 b= 2x+5
ab= (2x-3)(2x+5)
= 2x*2x+ 2x*5- 3*2x- 3*5
= 4x+ 10x- 6x- 15
= 14x- 6x- 15
= 8x -15
x= 2
= 8(2)- 15
= 16-15
= 1
Select the correct answer.
To solve this system of equations using substitution, what could be substituted in place of y in the first equation?
4x=5-2y
y-2x=7
Answer: y=2x+7
(this is a rearranged version of y-2x=7 from question)
Step-by-step explanation:
4x=5-2y
y-2x=7
i would rearrange the 2nd value into y intercept form y=mx+b
so move the -2x to the other side of the = sign by doing the opposite, +2x on both sides to isolate the y
y=2x+7
you didn't give any options for "correct answer" so i can't give
you A B C or D answers
What is the solution for x in the equation?
-2x+14+ 10x=34
OA. x = 6
OB. x = 5/2
OC. x = 1/8
OD. x = 2/5
Answer:
B. x = 5/2
Step-by-step explanation:
-2x+14+ 10x=34
-2x+10x=34-14
8x=20
x=20/8 =5/2
A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.2 meters per week. After 7 weeks, the sheet is only 2.4 meters thick.
Let y represent the ice sheet's thickness (in meters) after x weeks.
Complete the equation for the relationship between the thickness and number of weeks.
y=_____
The equation for the relationship between the thickness and number of weeks is y = 3.8 - 0.2x
How to write equation?Ice lost per week = 0.2 metersIce remaining after 7 weeks = 2.4 metersNumber of weeks = xRelationship between the thickness and number of weeks = yIce lost at 7 weeks = 7(0.2) = 1.4 meters
Total thickness of ice before loss = Ice remaining after 7 weeks + Ice lost at 7 weeks
= 2.4 + 1.4
= 3.8 meters
The equation:
y = Total thickness of ice before loss - (Ice lost per week × Number of weeks)
= 3.8 - (0.2 × x)
y = 3.8 - 0.2x
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The graph below represents the result of a survey in which a number of students
reported how many letters were in their last names.
What was the range of name lengths?
The range of name lengths is equal to 8.
What is a range?In Mathematics and Statistics, a range can be defined as the difference between the highest number and the lowest number contained in a data set.
In Mathematics and Statistics, the range of a data set can be calculated by using this mathematical expression;
Range = Highest number - Lowest number
From the given data set, we have:
Highest number = 10.
Lowest number = 2.
By substituting, we have:
Range = 10 - 2
Range = 8.
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If you pull a card from a standard deck of 52 and then pull a second card without replacing the first card, you have about a ____ chance(round to nearest percent) of pulling out a face card, followed by on ace.
The probability that you pull a card from a standard deck of 52 and then pull a second card without replacing the first card is 2%
How to determine the probability?The given parameters are:
Cards = 52
Face card = 12
Ace = 4
The probability of selecting a face card is:
P(Face card) = 12/52
Now, there are 51 cards.
The probability of selecting an ace is:
P(Ace) = 4/51
The required probability is:
P = 12/52 * 4/51
Evaluate
P = 0.0181
Express as percentage
P = 1.81%
Approximate
P = 2%
Hence, the probability is 2%
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Given: ΔABC (to the right)
AB=15
BD=9
AD⊥BC
m∠C=30°
Find Perimeter of ABC
Applying the Pythagorean theorem and the trigonometric ratios, the perimeter of triangle ABC is: 68.8 units.
What is the Perimeter of a Triangle?The perimeter of a triangle = sum of its 3 sides.
Given the following:
AB = 15 BD = 9m∠C=30°Use the Pythagorean theorem to find AD considering triangle ADB as a right triangle:
AD = √(15² - 9²)
AD = 12 units
Use the trigonometric ratios to find DC and AC:
sin 30 = AD/AC
sin 30 = 12/AC
AC = 12/sin 30
AC = 24 units
tan 30 = AD/DC
tan 30 = 12/DC
DC = 12/tan 30
DC ≈ 20.8 units
BC = BD + DC = 9 + 20.8
BC = 29.8 units.
Perimeter of triangle ABC = BC + AB + AC
Perimeter of triangle ABC = 29.8 + 15 + 24
Perimeter of triangle ABC = 68.8 units.
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help me please I will give you brainliest
Answer:
-17, -10, -6, -5, 3, 8 only change is between 3 and 8
Explain how the expression 32 relates to the diver's depth
Answer:
See below
Step-by-step explanation:
Each 32 feet of depth is 1 more atmosphere of pressure on the diver
hat is the slope of the linear relationship shown in this table of values?
x y
-4 11
2 -1
5 -7
By using any two of the points in the table, we will see that the slope is -2.
How to get the slope for the linear relationship?
A general linear relationship is:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that if the line passes through (x₁, y₁) and (x₂, y₂), the slope is:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we can use the first two points on the table:
(-4, 11) and (2, -1), so the slope is:
[tex]a = \frac{11 - (-1)}{-4 - 2} = 12/-6 = -2[/tex]
Then the slope of the line is -2.
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The regular price of a tennis racquet is $79.99 and the sale price is $64.99. Find the percent of discount to the nearest whole percent.
Step-by-step explanation:
$79.99 - $64.99 = $15
(79.99 - 64.99)/|79.99| =15
15/79.99 =
15 ÷ 79.99 =
15 ÷ 79.99 × 100/100 =
(15 × 100 ÷ 79.99)/100 =
(1,500 ÷ 79.99)/100
≈18.752344043005/100 =
18.752344043005% ≈18.75%;
Part E
Use the table showing Manuel's and Gretchen's data to determine the mean, median, standard deviation, and
interquartile range for each data set. Use this information to complete the second table. Use the graphing tool to
determine the value of standard deviation.
The mean, median, standard deviation, and interquartile range for each data set is given below.
What is the definition of Interquartile Range (IQR)?When arranged from lowest to highest, the IQR represents the central 50% of values.
Find the median (middle value) of the lower and higher half of the data to get the interquartile range (IQR).
These are the quartile 1 (Q1) and quartile 3 (Q3) values (Q3). The difference between Q3 and Q1 is the IQR.
What are the measures of central tendency for Manuels Data?Using the statistical tool, the following were arrived at:
Standard Deviation = 3.13961Mean = 8Median = 8IQR = Q3-Q1 = 10 - 6 = 4What are the measures of central tendency for Grethcen's Data?Using the statistical tool, the following were arrived at:
Standard Deviation = 4.68737.Mean = 9.6Median = 9IQR = IQR = Q3-Q1 = 12 - 7 = 5.See the respective Histograms attached.
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The endpoints of wx are w (5,-3) and x (-1,-9) what is the length of wx ?
Using the distance formula, the length of WX is approximately: 8.5.
How to Find the Length of a Segment Using the Distance Formula?Distance formula is, [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].
Given the endpoints:
W(5,-3) = (x1, y1)
X(-1,-9) = (x2, y2)
Plug in the values:
WX = √[(−1−5)² + (−9−(−3))²
WX = √[(−6)² + (−6)²]
WX = √72
WX ≈ 8.5
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Answer:
6 2 with the little check mark line in the midddle
Step-by-step explanation: