The standard deviation for the test is 8, the mean score is 79.
what is standard deviation?The standard deviation is a measurement of how much a group of values vary or are dispersed. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Given that,
On a science test, a score of 91 falls exactly 1.5 standard deviations above the mean.
μ + 1.5σ = 91
If the standard deviation for the test is 8
σ = 8
μ + 1.5σ = 91
μ + 1.5(8) = 91
μ + 12 = 91
μ = 91-12
μ = 79
Therefore, the mean score is 79.
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Two security cameras are positioned on the ceiling of a gym 10 m apart. When camera has an angle of depression of 50° to a point on the floor and the other camera has an angle of depression of 60° to the same point calculate the height of the gym.
When camera has an angle of depression of 50° to a point on the floor and the other camera has an angle of depression of 60° to the same point calculate the height of the gym, the height of gym is 7.05 m
What is angle of depression?When the observer is above the object they are looking at, an angle of depression is created. An angle below the horizontal line drawn with the level of the observer's eye and the line connecting the object with the observer's eye is created when an observer looks at an object that is placed at a distance lower than the observer.
Lets name the points on the triangles as A, B ,C
m∠ABC = 180° - 60° + 50°
= 70°
Now, the sine theorem defines
[tex]\frac{AB}{sin50\textdegree}[/tex] = [tex]\frac{AC}{sin70\textdegree}[/tex] = [tex]\frac{10}{sin70\textdegree}[/tex]
AB = 8.15 meters
Now using the area of triangle formula
area∠ABC = 1/2 × AB × AC × sin∠BAC = 1/2 × h × AC
⇒ 1/2 × 8.15 × 10 × √3/2 = 1/2 × h × 10
⇒ 8.15 × √3/2 = h
⇒ h = 7.05
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ignoring all other issues, how many pounds of grain supplement should farmer ben feed his cows if the price of milk is $0.20 per pound and the price of grain supplement is $0.70 per pound?
The most appropriate choice for profit and loss will be given by
Uncle Ben will feed his cows 2 pounds of grain supplement.
What is profit and loss?
If the selling price is more than the cost price, then the difference between the selling price and the cost price will give the profit.
If the selling price is less than the cost price, then the difference between the selling price and the cost price will give the loss.
Here,
For 1 pound
Cost price of grain supplement = [tex]0.70 \times 1[/tex]
= $[tex]$0.70[/tex]
Selling price of milk = [tex]0.20 \times 5[/tex]
= $[tex]1[/tex]
Profit = $([tex]1 - 0.70[/tex])
= $0.30
For 2 pounds
Cost price of grain supplement = [tex]0.70 \times 2[/tex]
= $[tex]$1.40[/tex]
Selling price of milk = [tex]0.20 \times 9[/tex]
= $[tex]1.80[/tex]
Profit = $([tex]1.80 - 1.40[/tex])
= $0.40
For 3 pounds
Cost price of grain supplement = [tex]0.70 \times 3[/tex]
= $[tex]$2.10[/tex]
Selling price of milk = [tex]0.20 \times 12.3[/tex]
= $2.46
Profit = $([tex]2.46 - 2.10[/tex])
= $0.36
For 4 pounds
Cost price of grain supplement = [tex]0.70 \times 4[/tex]
= $[tex]$2.80[/tex]
Selling price of milk = [tex]0.20 \times 15.5[/tex]
= $3.1
Profit = $([tex]3.1 - 2.80[/tex])
= $0.30
For 5 pounds
Cost price of grain supplement = [tex]0.70 \times 5[/tex]
= $[tex]$3.50[/tex]
Selling price of milk = [tex]0.20 \times 18[/tex]
= $3.60
Profit = $([tex]3.60 - 3.50[/tex])
= $0.10
For 6 pounds
Cost price of grain supplement = [tex]0.70 \times 6[/tex]
= $[tex]$4.20[/tex]
Selling price of milk = [tex]0.20 \times 20[/tex]
= $4
Loss = $([tex]4.20 - 4[/tex])
= $0.20
For 7 pounds
Cost price of grain supplement = [tex]0.70 \times 7[/tex]
= $[tex]4.90[/tex]
Selling price of milk = [tex]0.20 \times 21.5[/tex]
= $[tex]4.30[/tex]
Loss = $([tex]4.90 - 4.30[/tex])
= $0.60
For 8 pound
Cost price of grain supplement = [tex]0.70 \times 8[/tex]
= $[tex]$5.60[/tex]
Selling price of milk = [tex]0.20 \times 22.5[/tex]
= $[tex]4.50[/tex]
Loss = $([tex]5.60 - 4.50[/tex])
= $1.10
For 9 pounds
Cost price of grain supplement = [tex]0.70 * 9[/tex]
= $[tex]6.30[/tex]
Selling price of milk = [tex]0.20 * 23[/tex]
= $[tex]4.60[/tex]
Loss = $([tex]6.30 - 4.60[/tex])
= $1.70
Since profit from 2 pounds of grain supplement is the most, Uncle Ben will feed his cows 2 pounds of grain supplement.
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Complete Question
Farmer Ben knows that feeding a grain supplement to his cows will produce more milkaccording to the following schedule:
ignoring all other issues, how many pounds of grain supplement should farmer ben feed his cows if the price of milk is $0.20 per pound and the price of grain supplement is $0.70 per pound?
The table has been attached here
What is an equation of the line that passes through the points (−5,−7) and (-5, 6)?
Answer: x = -5
Both points have the same x value and only have different y values, meaning that the equation of the line must be x = -5.
Is the following relation a function?
A) Yes
B) No
Answer:
I say b
Step-by-step explanation:
|9-5| - |5-9|
A. -8
B. -6
C. -4
D. 0
E. 8
When calculating the modulus of a negative number, the minus sign is disregarded. The expression of |9-5| - |5-9| exists 0.
What is meant by the modulus function?A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count. A function with absolute values is another name for it. No matter what input was provided to this function, the outcome is always favorable.
When calculating the modulus of a negative number, the minus sign is disregarded. The modulus of a number is denoted by writing vertical lines around the number.
Let the expression be |9-5| - |5-9|
Subtracting the numbers, we get
|9-5| - |5-9| = |4| - |-4|
simplifying the above expression, we get
= 4 - 4
= 0
Therefore, the correct answer is option D. 0.
The complete question is:
Simplify |9-5| - |5-9|
A. -8
B. -6
C. -4
D. 0
E. 8
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A circle has a radius 12 mm. What is its area? use 3.14 to show your work.
10. Mrs. Hammonds made a deposit of $100 into her checking
account. Then she wrote checks for $97.54 and $48.27. If her
previous balance was $320.39, what is her new balance?
Previously available balance = $320.39
Deposit made by Mrs. Hammonds = $100
Cheques used for withdrawal,
$97.54
$48.27
The new balance = $320.39 + $100 - $97.54 - $48.27
= 420.39 - 145.81
= 274.58
So, the new balance in her account is $274.58.
What is Withdrawal?According to accounting terminology, a company withdrawal is the removal of funds, but not to compensate the owner as in an owner's draw. A withdrawal can be made for many different purposes, such as paying an employee back for a company expense or covering a cash-intensive business expense like entertaining a significant client at a sporting event. A withdrawal can also refer to the departure of money from an employer-sponsored retirement plan, like a 401k. Additionally, some businesses have a petty cash fund set up for various modest charges; certain incidental expenses may also be paid out of this account. An owner's draw or accounting drawing is not taxed in the traditional sense.To learn more about Withdrawal, refer to:
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The sum of three mixed numbers is 24 4/5. Two of the number are 8 2/3 and 6 5/6. What is the third number?
The numerical value of the third number in an improper and mixed fraction form is 93/10 and 9 3/10 respectively.
What is the value of the third number?Given the data in the question;
Let 'x' represent the third number
Sum of the three numbers = 24 4/5First number = 8 2/3Second number = 6 5/6Third number = xFirst, convert the numbers form mixed fractions to improper fractions
Sum of the three numbers = 24 4/5 = ( 24×5 + 4 )/5 = 124/5
First number = 8 2/3 = ( 8×3 + 2 )/3 = 26/3
Second number = 6 5/6 = ( 6×6 + 5 )/2 = 41/6
Now, to determine the third value, equate the sum of the three numbers to the total and solve for x
26/3 + 41/6 + x = 124/5
( 156 + 123 )/18 + x = 124/5
( 279 )/18 + x = 124/5
31/2 + x = 124/5
x = 124/5 - 31/2
x = ( 248 - 155 )/10
x = ( 93 )/10
x = 93/10
x = 9 3/10
Therefore, the value of the third number is 93/10 or 9 3/10.
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maths question photo attached
The exact area of the shaded region is: (2 - √6)/8 cm².
What is the Area of a Triangle?The area of a triangle = 1/2(base)(height).
The area of the shaded region = area of triangle ABD - area of triangle ACD.
Area of triangle ABD:
Base of triangle ABD = AD = √2/2
Height of triangle ABD = BD = √2/2
Area of triangle ABD = 1/2(√2/2)(√2/2)
Area of triangle ABD = 2/8 = 1/4 cm²
Area of triangle ACD:
Base of triangle ACD = AD = √2/2
Height of triangle ACD = CD = √3/2
Area of triangle ACD = 1/2(√2/2)(√3/2)
Area of triangle ACD = √6/8 cm²
Area of the shaded region = 1/4 - √6/8
Area of the shaded region = (2 - √6)/8 cm²
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5. Percent Word Problem
The original price of a chocolate bar was $25. During a store-closing sale, a shopper saved $3 on the
chocolate bar. What percentage discount did she receive?
The sales tax in your city is 4.4\%4.4%4, point, 4, percent, and an item costs \$3$3dollar sign, 3 before tax.
How much tax would you pay on that item?
Round to the nearest hundredth or cent.
The tax that is paid on the item purchased to the nearest cent is $0.13,
What is the tax paid?Tax is a form of transfer of wealth from individuals or businesses to the government. Taxes increase the cost of a good or service. When tax is levied on a good or service, the tax is paid when the good or service is paid for. It is added to the purchase price of the good or service.
In order to determine the tax paid, multiply the cost of the item by the tax rate. Multiplication is the process that is used to determine the product of a number. The sign that denotes multiplication is ×.
Tax paid = cost of the item x tax rate
$3 x 4.4%
$3 x 0.044 = $0.13
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 on January 14, the temperature in Anchorage, Alaska was -13 degrees. On the same day, there was a Polar Vortex over the northeast, and there was a recorded temperature of -24 degrees in Caribou, Maine. What Integer can be used to represent the difference in the two temperatures
The integer that can be used to represent the difference in the two temperatures is -37°.
How to calculate the temperature?From the information, the temperature in Anchorage, Alaska was -13 degrees and on the same day, there was a Polar Vortex over the northeast, and there was a recorded temperature of -24 degrees in Caribou, Maine.
Therefore, the integer can be used to represent the difference in the temperatures will be:
= -13 + (-24)
= -13 - 24
= -37
The difference in temperature is -37°.
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m is directly proportional to r squared. when r=2 m=14. work out the value of m when r=12
[tex]\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"m" proportional to }r^2}{ {\Large \begin{array}{llll} m=kr^2 \end{array}}}\qquad \textit{we also know that} \begin{cases} r=2\\ m=14 \end{cases}\implies 14=k(2)^2 \\\\\\ \cfrac{14}{2^2}=k\implies \cfrac{7}{2}=k\hspace{15em}\boxed{m=\cfrac{7}{2}r^2} \\\\\\ \textit{when r=12, what is "m"?}\qquad m=\cfrac{7}{2}(12)^2\implies m=504[/tex]
Please help!!! .The HCF of 90 and another number is 30. If the LCM of the number is 360, find the other number
Answer:
The other number is 120.
Step-by-step explanation:
30×360 =90xx
x=(30×360)/90
x=120
(HCFXLCM= Product if the two
numbers)
The multiples of 4 between 100 and 150
Answer:
104 ;108;112;116;120;124;128;132;136 ;140;144;148
Answer:
104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148
Step-by-step explanation:
A multiple of 4 can generally be defined as divisible by 4.
We can define an equation for it: [tex]4n[/tex] where n is an integer.
From here we can see that if n=25, we have a number of 100 which indeed is a multiple of 4 since dividing it by 4 results in 25 which makes sense since 100 is the result of 4 * 25.
Now starting from 100 (excluding 100 since between 100 and 150), or n=25, we can increase the value of the number by 4, or n by 1 which is doing the same thing.
So start at 100, then 100+4 = 104, then 104+4=108 and so on... until you reach a number greater than or equal to 150, and if it is 150 make sure to exclude it since it says between 100 and 150 which implies it's excluding the end points.
This gives us a result of: 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148
Hunter paid $44.20 for 5.2 pounds of shrimp. What is the price per pound of the shrimp?
Answer:
$8.50 per pound
Step-by-step explanation:
[tex]44.20 \div 5.2 = 8.50[/tex]
Sum of 8 consecutive numbers is 124. Find the numbers
Give breif detail and description this question contains 15 points (will also mark as brainliest)
The 8 consecutive numbers are 12, 13, 14, 15, 16, 17, 18, 19 respectively.
What are algebraic expressions?Algebraic expressions are simply described as arithmetic expressions that are made up of arithmetic terms, constants, variables, factors and coefficients.
These expressions are also made up of arithmetic operations which includes;
ParenthesesBracketDivisionMultiplicationAdditionSubtraction, etcBased on the information given, we have;
x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 + x + 7 = 124
Now, collect like terms, we get;
8x + 28 = 124
8x = 124 - 28
Subtract like terms
8x = 96
To determine the value of x, make it the subject by dividing both sides by 8, we have;
8x/8 = 96/8
x = 12
Then,
x = 12
x + 1 = 13
x + 2 = 14
x + 3 = 15
x + 4 = 16
x + 5 = 17
x + 6 = 18
x + 7 = 19
Hence, the values are 12, 13, 14, 15, 16, 17, 18 and 19 respectively.
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HELP PLS HAS TO BE TURNED IN IN 30 MINUTES
integrated 3 math
Describe the cross section formed by the intersection of a cone and a plane parallel to the base of the cone
Answer:
If you slice a cone parallel to the base, the cross section is a circle.
Step-by-step explanation:
ik this isn't all but i hope this helps
In a large population, 56% of the people have been vaccinated. If 5 people are randomly selected, what is the probability that at least one of them has been vaccinated?
The likelihood that someone has received a vaccination equals one minus the likelihood that no one has. The likelihood that a randomly chosen individual in a large population IS NOT immunized = 1 - 0.54 = 0.46.
The likelihood that the three randomly chosen individuals are not all immunized is 0.463, hence the likelihood that at least one of them has been immunized is 1 - 0.463.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
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A green marble is selected at random from a bag of 4 yellow, 3 green, and 9 blue marbles and not replaced. What is the probability a second marble selected will be green
haley pays a monthly fee of $20 for her cell phone and then pays 5 cents per minute used. the total cost of haley’s monthly cell phone bill can be expressed by the function c(m)
Agda, Britta and Cornelia must pay a bill together. Britta scabetala half as much as Agda. Cornelia must pay SEK 1,500 less than Britta. Agda must pay five times as much as Cornelia. Calculate how much Britta will pay.
The amount of money that Britta will pay is; SEK2500
How to solve Algebra Word Problems?Let the amount paid by Britta scabetala be x
Now, we are told that Britta scabetala half as much as Agda. Thus;
Amount paid by Agda = 2x
Now, Cornelia must pay SEK 1,500 less than Britta. Thus,
Amount paid by Cornelia = x - 1500
Agda must pay five times as much as Cornelia. Thus;
2x = 5(x - 1500)
2x = 5x - 7500
5x - 2x = 7500
3x = 7500
x = 7500/3
x = SEK2500
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6. What is the solution set of the inequality below? *х-x + 2>-72O x5-82O x2-8O x2-9/2O X28
Multiply both sides by 2:
[tex]x+2\ge-14-x[/tex]Add x to both sides:
[tex]2x+2\ge-14[/tex]Subtract 2 from both sides:
[tex]2x\ge-16[/tex]Divide both sides by 2:
[tex]\begin{gathered} x\ge-\frac{16}{2} \\ x\ge-8 \\ \end{gathered}[/tex]Answer:
[tex]x\ge-8[/tex]Alonso has $460 to spend at a bicycle store for some new gear and biking
outfits. Assume all prices listed include tax.
• He buys a new bicycle for $270.71.
• He buys 4 bicycle reflectors for $3.09 each and a pair of bike gloves for
$33.71.
• He plans to spend some or all of the money he has left to buy new biking
outfits for $68.20 each.
Write and solve an inequality which can be used to determine x, the number
of outfits Alonso can purchase while staying within his budget.
Answer:
Step-by-step explanation:
Answer:
In the solution below
Step-by-step explanation:
According to the question.
$257.62 + $18.19 × 2 + $11.18 = $305.18
$400 - $305.18 = $154.82
$154.82 ÷ $77.41 = 2
So she can buy 2 new biking outfits
I hope this helps you
:)
SECOND TIME ASKING HELP!!!
EASY POINTS WILL GIVE BRAINLIST TO BEST ANSWER Determine if the sequence is arithmetic. If it is, find the common difference, the 21st term, the explicit rule, the recursive rule, and the three terms in the sequence after the last one given. 7, 4, 1, -2, ...
Answer:
Yes, this is an arithmetic sequence.
The difference is -3, so a(n+1) = a(n) - 3
The 21st term is -53, calculated as follows:
a(21) = 7 + (21 - 1)(-3) = -53
The next three terms are -5, -8, and -11.
A scientist is determining the mass of 22000 molecules of oxygen. How many significant digits should be in the solution?
Based on the mass of the molecules of oxygen that the scientist determined, the number of significant digits in the solution is 2.
How to count significant digits?When counting the significant figures in a number, the first rule is that any digit that isn't a zero would be considered a significant digit.
Zeros that are trailing in a number however, and are not considered decimals, are not counted as significant digits. This means that both the 2 number 2s in the figure will be significant figures.
The three zeros are trailing but not decimals so they are not considered significant. This means that in the mass of oxygen according to the scientist, has only 2 significant figures.
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The points A(0,5), B(4,2), and C(0,2) form the vertices of a right triangle in the coordinate plane.
What is the equation of the line that forms the hypotenuse?
The equation of the line that forms the hypotenuse is y = -3/4 x + 5
Equation of a lineA line is defined as the shortest distance between two points. The equation of a line in slope-intercept form is expressed as:
y = mx + b
where:
m is the slope
b is the intercept
The coordinate points that gives the largest distance will be used. the points form the largest distance;
Using the coordinate points A(0,5), B(4,2)
Slope = 2-5/4-0
Slope = -3/4
The intercept is (0,5)
Determine the equation
y = mx + b
y = -3/4 x + 5
This gives the required equation.
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ILL MARK BRAINLIEST
What is the contrapositive of the following statement?
"If it does not have four legs, then it is a fish."
If it is a fish, then it does not have four legs.
If it has four legs, then it is not a fish.
If it is not a fish, then it has four legs.
If it does not have four legs, then it is not a fish.
Answer:
The answer is "If it does not have four legs, then an animal is not a fish
To form the contrapositive, switch the hypothesis and the conclusion and negate both.
The hypothesis is the "if" part and the conclusion is the "then" part.
Answer:
If it is not a fish, then it has four legs.
Step-by-step explanation:
If A then B
the contrapositive of this is
If Not B then not A.
Solve w=--Z
solve for x
When you solve w = __Z,
you will get the value of X ( but there should be a variable' X' in the blank space). This is the method in Algebra.
What is Algebra?When we employ words and numbers to answer a specific mathematical issue, this is known as an algebraic expression.Example , X = 5 + Z (If the value of Z is given we can easily find out the value of X)The alphabets are known as variables.To learn more about Algebra refer:
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The perimeter of the figure below is 122.7 ft. Find the length of the missing side.
?
14.9 ft
19.9 ft
6.5 ft
39.8 ft
6.5 ft
14.9 ft
14.9 ft
Answer:5.3ft
Step-by-step explanation: 1. find the sum of the rest of the sides
14.9+19.9+6.5+39.8+6.5+14.9+14.9=117.4
2. subtract 117.4 from 122.7 to find the missing side length
122.7-117.4=5.3