Answer:
the answer is -7+-25=-32
the equation of lime 1 is 3x-2y=5, and the equation of lime 2 is x+2y=7. What is the point of intersection of the two lines?
To find the point of intersection for two lines, we can use substitution to solve for the coordinates.
Solving the QuestionWe're given:
[tex]3x-2y=5[/tex][tex]x+2y=7[/tex]With these two equations, we can:
First isolate x in the second equationUse substitution to input in second equation into the first and solve for yUse the y-coordinate to find the corresponding x-coordinate using substitutionIsolate x in the second equation:
[tex]x+2y=7\\x =7-2y[/tex]
Substitute the second equation into the first:
[tex]3x-2y=5\\3(7-2y)-2y=5\\21-6y-2y=5\\21-8y=5\\21-8y=5[/tex]
Solve for y:
[tex]21-6y-2y=5\\21-8y=5\\-8y=-16\\y=2[/tex]
Solve for x:
[tex]x+2y=7\\x+2(2)=7\\x+4=7\\x=3[/tex]
AnswerThe point of intersection of the lines is (3,2).
Patrisse and Makayla began arguing about who did better on their tests, but they couldn't decide who did better given that they took different tests. Patrisse took a test in English and earned a 81.4, and Makayla took a test in Art History and earned a 60.6. Use the fact that all the students' test grades in the English class had a mean of 72.8 and a standard deviation of 11.8, and all the students' test grades in Art History had a mean of 67 and a standard deviation of 8.6 to answer the following questions. a) Calculate the z-score for Patrisse's test grade. z = [Round your answer to two decimal places.] b) Calculate the z-score for Makayla's test grade. z = [Round your answer to two decimal places.] c) Which person did relatively better? Patrisse Makayla They did equally well.
a) Z-score for Patrisse test grade is 0.7288
b) z-score for Makayla test grade is -0.7441
c) Patrisse did better.
What is z- score?
A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.
Z-score for Patrisse test grade.
X= 81.4, [tex]\mu[/tex] = 72.8, [tex]\sigma[/tex] = 11.8
Z= x- [tex]\mu[/tex] / [tex]\sigma[/tex]
Z= 81.4 - 72.8/ 11.8
Z= 0.7288
Now, z-score for Makayla test grade.
X= 60.6, [tex]\mu[/tex] = 67, [tex]\sigma[/tex] = 8.6
Z= x- [tex]\mu[/tex] / [tex]\sigma[/tex]
Z= 60.6 - 67/ 8.6
Z= -0.7441
Hence, Patrisse did better as she had better z- score.
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binomial expansion of (2+3x)^5
Angle PQT and Angle SQR are supplementary angles. If the measure of PQT is (3x+43)° and the measure of Angle SQR is (6x-25)°, what is the numeric measure of Angle PQT and Angle SQR?
Answer:
∠PQT = 97°
∠SQR = 83°
Step-by-step explanation:
Supplementary angles sum to 180°
⇒ ∠PQT + ∠SQR = 180°
Given:
∠PQT = (3x + 43)°∠SQR = (6x - 25)°Therefore:
⇒ (3x + 43) + (6x - 25) = 180
⇒ 3x + 6x + 43 - 25 = 180
⇒ 9x + 18 = 180
⇒ 9x = 162
⇒ x = 18
Substitute the found value of x into the expression for each angle:
⇒ ∠PQT = (3x + 43)°
⇒ ∠PQT = (3(18) + 43)°
⇒ ∠PQT = 97°
⇒ ∠SQR = (6x - 25)°
⇒ ∠SQR = (6(18) - 25)°
⇒ ∠SQR = 83°
Check
⇒ ∠PQT + ∠SQR = 97° + 83° = 180°
the line y=-3x+4 is reflected on the y-axis what is the equation of the reflected line
Answer:
x=0
Step-by-step explanation:
when the reflection falls on the y-axis the answer is x=0
URGENT 30 points I need help
Answer:
- 112 + 100 n
Step-by-step explanation:
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1 )d
~~~~~~~
[tex]a_{1}[/tex] = - 12
d = 100
[tex]a_{n}[/tex] = - 12 + 100( n - 1 )
[tex]a_{n}[/tex] = - 12 + 100n - 100
[tex]a_{n}[/tex] = - 112 + 100 n
833.30/
1-(1+0.00833)^-360
Answer:
833.25 or 877.59
Step-by-step explanation:
I solved this in two different ways because I wasn't sure on how the question was meant to be read.
Attempt 1:
(833.3/1)-(1+0.00833)^-360
(1+0.00833)^-360 = 0.0505
so:
833.3 - 0.0505 = 833.25
Attempt 2:
833.3/(1-(1+0.00833)^-360)
1- 0.0505 = 0.9495
833.3/0.9495 = 877.59
The ratio of (1/5 of 245ml) to (0.2 of 0.84l)
The ratio is given by 98:0.34.
The ratio of (1/5 of 245ml) to (0.2 of 0.84ml).
What is the Ratio?The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
we have (1/5 of 245ml) to (0.2 of 0.84ml).
⇒ [tex]\frac{1}{5} 245 :0.2*0.84[/tex]
⇒[tex]98:0.34[/tex]
Thus, the required ratio is 98:0.34.
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HELP! ASAP!
2.A cube-shaped plant box has edges that are 13 cm long. The plant box is filled with potting soil that has a density of 1.33 g/cm³.
(a) Is it safe to place the plant box on a window ledge that can support a maximum weight of 2400 grams? Explain why or why not.
(b) Would the density of the soil change if the plant box was only half full? Explain.
Step-by-step explanation:
2.
the volume of the box is
length × width × height = 13×13×13 = 13³ = 2197 cm³
the ratio of the density indignation tells us that every cm³ of soil weighs 1.33 g (or every unit of 1.33g soil fits into 1 cm³).
we have 2197 cm³.
their weight is
2197 × 1.33 = 2,922.01 g
so, the filled box clearly exceeds the max. weight of the window ledge, and it is NOT safe to put it there.
b
yes, it would be a little bit less dense.
because every bit of weight you put on top of something increases the pressure on and therefore the density of that something.
What is the slope of this line? the equation for a line that passes through the points (5,-3) and (-10,15)?
Part 1: Finding slope
The slope is [tex]\frac{-3-15}{5-(-10)}=\frac{-18}{15}=\boxed{-\frac{6}{5}}[/tex]
Part 2: Finding the equation
Using the point (-10, 15) to substitute into point-slope form,
[tex]y-15=-\frac{6}{5}(x+10)\\\\y-15=-\frac{6}{5}x-12\\\\\boxed{y=-\frac{6}{5}x+3}[/tex]
Answer:
Using the given points we find that the slope is -1.2 and using the slope-point form we find that the equation of line is y+1.2x = 3.
Step-by-step explanation:
In the question, two points are given, (5,-3) and (-10,15). Using them we can find the slope using the formula, (y2 - y1) / (x2 - x1). So, the slope is
(-3-15) / (5+10) = -18 / 15 = -1.2
Now, we have to find the equation of line. We have two points and a slope. Using any one point and the slope, we can find the equation of line using slope-point form of line. Let us take (5,-3).
(y+3) / (x-5) = -1.2
y+3 = -1.2(x-5)
y+3 = -1.2x + 6
y+1.2x = 3
So, the slope of line is -1.2 and the equation of line is y+1.2x = 3.
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Base of a prism is a right triangle with legs 3 feet and 4 feet. The height is 13 feet , what is the volume?
Answer:
Triangular prisms
Remember the formula for calculating volume is: Volume = Area by height. V = A X h.
For a triangle the area is calculated using the formula: Area = half of base by altitude. A = 0.5 X b X a.
So to calculate the volume of a triangular prism, the formula is: V = 0.5 X b X a X h
Step-by-step explanation:
The graph shows the function f(x) = 2x.
What is the value of x when f(x) = 8?
[tex]\large\orange\implies \rm \large \:f(x) \: = \: 2x[/tex]
We have to find x when f(x) is 8
[tex]\large\orange\implies \rm \large \:8 = \: 2x[/tex]
[tex]\large\orange\implies \rm \large \: \cancel\frac{8}{2} \: = \: x \\ [/tex]
[tex]\large\orange\implies \rm \large \: \: 4 \: = \: x[/tex]
The value of x is 4 when f(x) is 8[tex]f(x) \: = \: 2x[/tex]
We have to find x when f(x) is 8
[tex]8 = \: 2x[/tex]
[tex]x = \frac{8}{2} \\ \\ x = 1.[/tex]
The value of x is 4 when f(x) is 8 .
PLEASEEEEEEE PLEASEEEEEE HELPPPPPP ASAPPPP
Find the measure of angle A in degrees.
Answer:
Angles are 45, 45 and 90 degrees because
AB and BC are congruent so that means the angles eating the sides are also congruent.
So to find the congruent angles:
180-90=90/2=45 degrees
To find AC:
a²+b²=c²
x²+x²=h²
√18=√c²
3√2=c
(I don't know why it says 3√3, but I think the q is wrong)
Hope it helps!
Answer:
45 degrees
Step-by-step explanation:
This is a special right triangle with these lengths. Which leads us to find the angles of 45, 45, 90 and B is 90 so A and C are 45 degrees.
if A={4,7,10,13,17} and B={3,5,7,9}, then which of the following statements is true
A U B= {7}
B c A
B c B
Answer:
good questing it is something
Step-by-step explanation:
1-1-2- --3--1234-3
3-4
Q-
-4
-24
-4
-
q 43-
43-
3 4-3
4-
4-4
- answer is 2def not cap i need 5 poinnts i gues
Which values are part of the solution set? Check all that apply. x = 3 x = –5 x = negative one-half x = –4.5 x = –4
The values that are part of the solution are x = -5 and x = -4.5
Number linesNumber lines are lines that are used to represent the solution to inequalities.
From the given number line with he solution x > -4, this shows that all the solutions must be values that are greater than -4.
The values that are part of the solution are x = -5 and x = -4.5
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Liz earns a salary of $2,200 per month, plus a commission of 5% of her sales. She wants to earn at least
$2,500 this month. Enter an inequality to find amounts of sales that will meet her goal.your
variable represents. Enter the commission rate as a decimal.
Answer:
2200 + 0.5x >= 2500
Step-by-step explanation:
x is the amount of sales
Tioga Company manufactures sophisticated lenses and mirrors used in large optical telescopes. The
company is now preparing its annual profit plan. As part of its analysis of the profitability of individual
products, the controller estimates the amount of overhead that should be allocated to the individual product lines from the following information.
Lenses Mirrors
Units produced ................................................................................................................ 25 25
Material moves per product line ........................................................................................ 5 15
Direct-labor hours per unit ................................................................................................ 200 200
The total budgeted material-handling cost is $50,000.
Required:
1. Under a costing system that allocates overhead on the basis of direct-labor hours, the materialhandling costs allocated to one lens would be what amount?
2. Answer the same question as in requirement (1), but for mirrors.
3. Under activity-based costing (ABC), the material-handling costs allocated to one lens would be
what amount? The cost driver for the material-handling activity is the number of material moves.
4. Answer the same question as in requirement (3), but for mirrors.
Tioga Company manufactures sophisticated lenses and mirrors used in large optical telescopes, the values are mathematically given as
MH1=$1,000MH2=$1,000MH3=$1500MH4=$1500What is the material handling costs allocated?Generally, the equation for Material-handling cost for one lens mathematically given as
MH1=Total projected costs for material handling /{Total number of direct labor hours x Direct labor hours per unit)
MH1={$50,000/10.000)x 200
MH1=$1,000
2)
Material-handling cost for one mirror
MH2=Total budgeted material handling cost/ Total number of direct labor hours x direct labor hours per unit
MH2={$50,000/10.000)x 200
MH2=$1,000
3) Material-handling cost per lens
[tex]MH3=\frac{Total projected costs for material handling}{\frac{Number of material moves per lens + Number of material moves per mirror}{(Total number of lenses)}}* Material moves per lens[/tex]
[tex]MH3=\frac{50,000}{\frac{5+15}{25}}*5[/tex]
MH3=$1500
4)
[tex]MH4=\frac{Total projected costs for material handling}{\frac{Number of material moves per mirror + Number of material moves per lens}{(Total number of mirror)}}* Material moves per mirror[/tex]
[tex]MH4=\frac{50,000}{\frac{5+15}{25}}*5[/tex]
MH4=$1500
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what is the Smallest numbers :
p = x^2 + 2x +2 / x+1 (x>-1)
t= 1/x + 4/1-x (0
Answer:
I exactly don't know the answer
Evergreen Landscaping bought 4 tons of topsoil and 3 tons of mulch for $1460. The next week the
firm bought 5 tons of topsoil and 2 tons of mulch for $1391. Find the price per ton for each item.
Answer: The price per ton of topsoil is $179
and price per ton of mulch is $248.
Step-by-step explanation:
Let price of 1 ton of topsoil be x
and price 1 ton of mulch be y
According to question
4x + 3y = $1460 -(i)
and 5x + 2y = $1391 -(ii)
Now solving these linear equations
By multiply (i) equation with 5 and divide it by 4
we get 5x + [tex]\frac{15}{4}[/tex]y = $1825 -(iii)
Subtract equation (ii) from equation (iii)
5x +[tex]\frac{15}{4}[/tex] y - 5x - 2y = $1825-$1391
[tex]\frac{7}{4}[/tex]y=$434
y = $434х[tex]\frac{4}{7}[/tex] = $248
put value of y in equation (i)
4x + 3($248) = $1460
4x - $744 =$1460
4x = $716
x = $179
The price per ton of topsoil is $179
the price per ton of mulch is $248.
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Solve the compound inequality. Graph the solution set and write it in interval notation. x<2 and x>-3
Answer:
Answer is (-3, 2)
i need help. Part A: Create a five-number summary and calculate the interquartile range for the two sets of data. (5 points)
Part B: Are there any outliers present for either data set? Justify your answer mathematically. (5 points)
Five number summary and IQR of both the data sets are different.
For school A: Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17, IQR=9.5
For school B: Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19, IQR=7.5
No, the box plots are not symmetric.
Part A:
The given data sets are
School A : 9,14,15,17,17,7,15,6,6
School B : 12,8,13,11,19,15,16,5,8
Arrange the data in ascending order.
School A : 6,6,7,9,14,15,15,17,17
School B : 5,8,8,11,12,13,15,16,19
Divide each data set into four equal parts.
School A : (6,6),(7,9),14,(15,15),(17,17)
School B : (5,8),(8,11),12,(13,15),(16,19)
For school A:
Minimum=6, Q₁=6.5, Median= 14, Q₃=16, Maximum=17
The interquartile range of the data is
For school B:
Minimum=5, Q₁=8, Median= 12, Q₃=15.5, Maximum=19
[tex]IQR=Q_3-Q_1\\ =Q_3-Q_1\\ =16-6.2\\ =9.5[/tex]
The interquartile range of the data is
[tex]IQR=Q_3-Q_1\\ =Q_3-Q_1\\ =15.5-8\\ =7.5[/tex]
Part B:
The box plots are not symmetric because the data values are different. Five number summary and IQR of both the data sets are different.
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Given the following functions, find and simplify (f+g)(-2).
Do not include "(f+g)(-2)=" in your answer.
f(x) = -3x² - 2x
g(x) = -2x +3
Answer:
43
Step-by-step explanation:
because if you add it up thats how you get that
What is the multiplicative rate of change between 10,50 and 250
Answer:D
Step-by-step explanation:
Camp pine cone has 20 campers for every 6 counselors if there are 60 campers how many counselors are needed
Answer:
18
Step-by-step explanation:
20*3=60 so do 6*3 to get your answer
Determine whether or not each of the following is a partition of set N of natural numbers. (With reason)
(a) {{n | n > 5}, {n | n < 5}]
(b) [{n | n > 6}, {1, 3,5} , {2, 4}]
(c) {{n | n^2 > 11}, {n | n^2 < 11}
Only Set B is a partition of set N of natural numbers .
What are Natural Numbers ?Numbers starting from 1 to infinity comes under Natural Numbers.
It is asked in the question that to determine whether or not each of the following is a partition of set N of natural numbers
A ) {{n | n > 5}, {n | n < 5}]
It is not a set of natural numbers as it does not include 5.
B ) [{n | n ≥ 6}, {1, 3,5} , {2, 4}]
{1,3,5} {2,4}and {n|n≥6} include all the natural numbers
Therefore , it forms a partition of N.
C ) {{n | n^2 > 11}, {n | n^2 < 11}
Every natural number n must satisfy either n^2 > 11 or n^2 < 11
This cannot be possible , therefore it is not the partition of Natural Numbers.
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A student has a test scores of 87, 89, 94 points. What must he score on the fourth exam to have an average of at least 92 points?
Answer: He must have atleast 98 points on the next exam in order to get an average of 92 points.
Step-by-step explanation: To calculate average, you need to add all the numbers given, and divide the sum by how many numbers there are. 87 + 89 + 94 + 98 (equals 368), and divide 368 by 4. You will get the average of 92 as its result.
The power of an exponential expression raised to a power is the product of the exponents.
Answer:
[tex](y {}^{c} ) {}^{d } = y {}^{c \times d} \\ = y {}^{cd} \\ \\ \\ \\ \\ (v {}^{3} ) {}^{7 } \\ = v {}^{3 \times 7} \\ = v {}^{21} [/tex]HOPE THAT HELPS.Put the steps in order to solve the literal equation for y in terms of x.
6x+2y+ 8 = 180
Answer:
x = [tex]\frac{172-2y}{6}[/tex]
Step-by-step explanation:
6x + 2y + 8 = 180 ( subtract 8 from both sides )
6x + 2y = 172 ( subtract 2y from both sides )
6x = 172 - 2y ( divide both sides by 6 )
x = [tex]\frac{172-2y}{6}[/tex]
Can someone please solve
Answer: [tex]\sqrt{7}[/tex]
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]3^2 + b^2 = 4^2\\\\9+b^2 = 16\\\\b^2 = 7\\\\b=\boxed{\sqrt{7}}[/tex]
3a =2b + -6 (solve for a)
Answer:
shown below
Step-by-step explanation:
3a = 2b - 6
a = (2b - 6) / 3 or 2b / 3 - 2
Answer:
a = (2b-6)/3
Step-by-step explanation:
3a = 2b + -6
lets make a the subject of the formula
divide both sides of the equation by 3
3a/3 = a = (2b-6)/3
a = (2b-6)/3
