In mixed fraction the total distance of the fun run is 11 1/14
A school is organising a fun run. The fun run involves a 5 1/2
mile run around the field, then a 5 4/7 mile run back to the school.
The total distance is equal to summation of run around the field and run back to school.
total distance = 5 1/2 + 5 4/7
= 11/2 + 39/7
The L. C. M of 2 and 7 is 14
= [tex]\frac{11.7}{2.7} + \frac{39.2}{7.2}[/tex]
(77 + 78)/14
155/14
Upon dividing 155 by 14, the quotient is 11 and the the remainder is 1
In mixed fraction it is 11 1/14
So in mixed fraction the total distance of the fun run is 11 1/14
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According to the Housing Recommendations, if a family has a gross annual income of $52,000, what is the maximum amount of a mortgage loan the family could afford?
State your answer in terms of dollars, but do not include a $ sign or the word "dollars" with your response.
Eric had $197 in his savings account before he was paid his weekly salary. His current savings balance is $429. How much money does Eric earn each week? (Form an equation.)
Answer:
[tex]197+\text{ n= 429}[/tex]Explanation:
Here, we want to get the amount of money Eric earns per week
Let the amount earned be n
Now, to get the value earned, we have to subtract the value he had before from what he has now or simply add what he had before to what he earned now and equate to his total balance now
Mathematically, we have that as:
[tex]197\text{ + n = 429}[/tex]There are 8 grams of pure drug in 75 milliliters of solution. What is the precent strength of solution? Round tothe nearest hundredth
Step 1: Let's review the information given to us to answer the exercise correctly
Amount of pure drug in the solution = 8 grams
Amount of solution = 75 mL
Step 2: Let's answer the question, as follows:
Percent strength of the solution = Amount of pure drug in the solution/Amount of solution * 100
Replacing with the values we know:
Percent strength of the solution = 8/75 * 100
Percent strength of the solution = 0.10666 * 100
Percent strength of the solution = 10.67% (Rouding to the next hundredth)
Tenth = one decimal place
Hundreth = two decimal places
Thousandth = three decimal places
What should be done to both sides of the equation in order to solve 1/3 x=4? Divide by 4Multiply by 4 Divide by 1/3Multiply by 1/3
The given equation is,
[tex]\frac{1}{3}x=4[/tex]So, from this equation , we have to find the value of x. The left hand side of the equation has x with 1/3 as coefficient, therefore, inorder to make it x, we have to,
[tex]\frac{1}{3}x\times3\rightarrow x[/tex]as the thress get cancelled. If we do some operation on one side of the equal sign, it is to be applied on the other side also so as to maintain the equivalency.
So here we have to multiply by 3.
But in option, there is no as such given , but it is given that divide by 1/3.
[tex]\frac{\frac{1}{3}x}{\frac{1}{3}}\rightarrow\frac{1}{3}x\times3^{}^{}[/tex]which is equuivalent to multiplying by three.
So the option " Divide by 1/3" is correct.
The effectiveness of a blood-pressure drug is being investigated. An experimenter finds that, on average, the reduction in systolic blood pressure is 52.4 for a sample of size 25 and standard deviation 8.5. Estimate how much the drug will lower a typical patient's systolic blood pressure (using a 98% confidence level). Assume the data is from a normally distributed population.
Enter your answer as a tri-linear inequality accurate to three decimal places.
answer < μ < answer
The patient's systolic blood pressure will be lowered by 48.709< m<56.091 at a 98% confidence interval.
What is a confidence interval?
For an unknown parameter, a confidence interval is just a range of guess. Usually 95% confidence level is generally the most usual, but other levels, such 90% or 99%, are occasionally used to generate a Confidence interval.The reduction in systolic blood pressure is, mean, x=52.4
Sample size, n=25
Standard deviation, s=8.5
We must determine the t value for a 90% Confidence interval because the sigma is unknown.
From Inverse t Distribution Calculator, the Confidence interval is 0.98 and the degree of freedom is 25-1=24:
One-sided t-Score: 2.1715
We can now determine the standard error E:
E=2.1715(8.5/√25)=3.691
We can now create the confidence interval by:
x - E < m < x+ E
52.4-3.691< m<52.4+3.691
48.709< m <56.091
The patient's systolic blood pressure will be lowered by 48.709< m <56.091 at a 98% confidence interval.
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Broad Street divides Popperville into an east side and a west side. On the east side of Popperville, 20% of the children qualify for a reduced-price lunch. On the west side of Popperville, 30% of the children qualify for a reduced-price lunch. Is it correct to calculate the percentage of children in all of Popperville who qualify for reduced-price lunch by adding 20% and 30% to get 50%? If the answer is no, why not? Explain in detail and calculate the correct percentage in at least two examples.
The two examples given in the question are therefore resolved, and the correct percentages are also computed.
Given:
Popperville is split into an east and a west side by Broad Street. 20% of the kids on Popperville's east side are eligible for free or reduced-price lunches. 30% of the kids on Popperville's west side are eligible for free or reduced-price lunches.
Consider a situation where the west side has 60% and the east side has 40%.
Example Number 1
There are 100 kids on East Side.
The 100 kids on West Side.
Children who qualify for reduced-price lunches at a rate of 20% out of 100
Children who qualify for reduced-price lunches at 30% of the total are 30.
Total percent is 50/200 = 25 %
Example Number 2
There are 200 kids on East Side.
There are 300 kids on West Side.
Children eligible for reduced-price lunches: 20% x 200 = 40
Children eligible for reduced-price lunches: 30% x 300 = 90
Total percentage is 130/500 = 26%.
As a result, the two examples given in the question are resolved, and the appropriate percentages are also computed.
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For the following, I have to find where the orthocenter, the centroid, and the circumcenter are within the diagram
Orthocenter
Let
A(2,0)
B(3,2)
C(6,0)
step 1
Find out the slope AB
m=(2-0)/(3-2)
m=2/1
m=2
Remember that
If two lines are perpendicular, then, their slopes are negative reciprocal
so
the slope of the altitude that passes through C is -1/2
Find out the equation of the altitude that passes through C
y=mx+b
we have
m=-1/2
point C(6,0)
substitute
0=-(1/2)(6)+b
solve for b
0=-3+b
b=3
equation is y=-(1/2)x+3 -------> equation 1
step 2
Find out the slope BC
m=(0-2)/(6-3)
m=-2/3
so
the slope of the altitude that passes through A is 3/2
Find out the equation of the altitude that passes through A
y=mx+b
we have
m=3/2
point A(2,0)
0=(3/2)(2)+b
solve for b
0=3+b
b=-3
y=(3/2)x-3 ------> equation 2
step 3
the intersection point equation 1 and equation 2 is the orthocenter
y=-(1/2)x+3 -----> equation 1
y=(3/2)x-3 ------> equation 2
solve the system
solve by graphing
using a graphing tool
the intersection point is (3,1.5)
that means
the orthocenter is (3,1.5)
see the attached figure to better understand the problem
Given f of x is equal to the quantity x plus 3 end quantity over the quantity x squared minus 4 times x minus 21 end quantity and g(x) = log4x, evaluate (g – f)(8).
The numeric value of the subtraction function at x = 8 is given by:
(g - f)(8) = 0.5.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the input variable in the function by the desired value.
To find the subtraction function, we find the numeric value of each function, then subtract them, as follows:
(g - f)(8) = g(8) - f(8).
Function f(x) is defined as follows:
f(x) = (x + 3)/(x² - 4x - 21).
At x = 8, the numeric value is given as follows:
f(8) = (8 + 3)/(8² - 4(8) - 21) = 11/11 = 1.
Function g(x) is defined as follows:
g(x) = log4(x).
At x = 8, the numeric value is given as follows:
g(8) = log4(8) = 1.5, as 4^(1.5) = 8.
Hence the numeric value of the subtraction function is given by:
(g - f)(8) = g(8) - f(8) = 1.5 - 1 = 0.5.
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What is the slope of the line passing through (0, 5) an d(-12, 2) ?
Enter your answer in the box.
The slope of the line passing through (0, 5) and (-12, 2) will be 1/4.
What is Slope?
A slope of a line is a number that describes both the direction and the steepness of the line.
Given that;
Two points on line are (0, 5) and (-12, 2).
Now, The slope of the line passing through (0, 5) and (-12, 2) are calculated as;
m = (2 - 5)/ (-12 - 0)
m = - 3 / -12
m = 3 / 12
m = 1/4
Thus, The slope of the line passing through (0, 5) and (-12, 2) will be 1/4.
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After how many days do only 4/5 of the students recall the important features of the classroom lecture? There are two parts to this questionIt says locate the point on the graph that conveys this information
Given:
[tex]P(x)=90-25log_2x[/tex]Required:
We need to find the value of x when P(x)=80.
Explanation:
[tex]Substitute\text{ P\lparen x\rparen=80 in the equation }P(x)=90-25log_2x.[/tex][tex]80=90-25log_2x[/tex]Solve for x.
[tex]25log_2x=90-80[/tex][tex]25log_2x=10[/tex]Divide both sides by 25.
[tex]\frac{25log_2x}{25}=\frac{10}{25}[/tex][tex]log_2x=\frac{2}{5}[/tex][tex]Use\text{ If }log_bx=y\text{ then }b^y=x.\text{ here b=2 and }y=\frac{2}{5}.[/tex][tex]x=2^{\frac{2}{5}}[/tex][tex]x=2^{0.4}[/tex][tex]x=1.3\text{ days.}[/tex]Final answer:
[tex]x=1.3\text{ days.}[/tex]See a horizontal line from point 80 on the y axis and mark the intersection point on the graph.
He is able to jog 600 meters every minute, keeping a constant speed. After jogging for 8 minutes, he stops to have a drink of water. If he has to jog 9,700 meters to get to work, then what should his constant pace be if he has no more than 15 minutes to get to work? Helppp
Based on the distance that has to be jogged to get to work, and the current speed, the constant pace that is needed to get to work is 327 meters per minute
How to find the constant pace?First, find out how much of the journey has already been jogged:
= Meters per minute x Number of minutes
= 600 x 8
= 4,800 meters
Distance left to get to work:
= 9,700 - 4,800
= 4,900 meters
The constant pace can be found by the formula for speed:
= Distance / time
= 4,900 / 15 minutes
= 327 meters per minute
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Given m/8= 86° and m/4= (4x + 2)°, what is the value of x ?
m∠4=m∠8 (Corresponding angles are equal)
[tex]4x+2=86\\4x=86-2\\4x=84\\\frac{4x}{4} =\frac{84}{4} \\x=21[/tex]
x=21°
lfp 3.1/ 3.2 practice
Divide fractions
3.1/3.2
PART 1,
Pithagorean theorem
x^2 =™9^2 + 12^2 = 81 + 144 = 225
then
x=√225 = 15
PART 2
x^2 = 10^2 + 24^2 = 100 + 576 = 676
then
x= √676 = 26
PART 3
10 ^ 2 = x^2 + 6^2
So then
10^2 - 6^2 = x^2
100 - 36 = x^2
64 = x^2
√64 = 8 = x
PART 4
24^2 = x^2 + 6^2
So then write
24^2 -6^2 = x^2
576 - 36 = x^2
As a result
540 = x^2
Then
√540 = x
Write the following inequalities in interval notation. Type “infinity” for infinity. A) c_<1 B) x<1.6 C) x_>9/2
Answer:
Explanations
Inequalities expressions are expressions not separated with an equal sign. The inequality signs are <, >, ≤ and ≥.
From the given question, we are to write the given inequality in interval notation.
Interval notation are represent using the set notation symtion sym
which of the following is a line of reflection for the image shown on the graph?
The line of reflection is the line that bisects the line joining any point on the shape ABC and a corresponding point on the shape A'B'C'.
S
Step 1: Find the gradient of the line AA'.
Suppose that a certain basketball athlete earned $20,750,000 to play 80 games, each lasting 48 minutes. (Assume no overtime games.)
a. How much did the athlete eam per game?
b. Assuming that the athlete played every minute of every game, how much did he earn per minute?
c. Assuming that the athlete played 2/3 of every game, how much did he earn per minute?
d. Suppose that, averaged over a year, the athlete practiced or trained 33 hours for every game and then played every minute. Including this
training time, what was his hourly salary?
a. The athlete earned S
b. The athlete earned $
(Round to the nearest dollar per minute as needed.)
per game.
per minute played if he played the entire game for every game.
c. The athlete earned $ per minute played if he played 2/3 of every game.
(Round to the nearest dollar per minute as needed.)
d. The athlete earned $ per hour if he trained 33 hours for every game and then played every minute. (Round to the nearest dollar per hour as
needed.)
Next
A) The athlete received $259,375 for each game.
B) The athlete was paid $540.64 per minute.
C) The athlete's hourly wage was $8105.46.
D) The athlete was paid $213,917.52 per hour.
A) Assume a basketball player received $20,750,000 for playing 80 games, each lasting 48 minutes.
X = 20,750,000 ÷ 80
X = 259,375
B) Assuming the athlete played every minute of every game.
X = 259375 ÷ 48
X = 5403.64
C) On the other hand, suppose the athlete performed in two-thirds of the games.
X = 259375 ÷ (48 x 2 ÷ 3)
X = 259375 ÷ 32
X = 8105.46
D) Finally, suppose that over one year, the athlete practiced or practiced 33 hours for each game and afterward played every moment of that time.
X = 20,750,000 ÷ (33 + (48 x 80 ÷ 60)
X = 20,750,000 ÷ (33 + 64)
X = 20,750,000 ÷ 97
X = 213,917.52
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Suppose that the base of the square pyramid below has an area of 14 cm2 and that the altitude of the pyramid measures 6 cm.A solid slanted to the left has vertices labeled A, B, C, D and E.Vertex E is located above and to the left of vertices A, B, C, and D.A segment extends from the top vertex, E, to each of the other vertices: A, B, C, and D.A square is formed by vertices A, B, C, and D.Find the volume (in cubic centimeters) of the square pyramid. Incorrect: Your answer is incorrect. cm3
Explanation
The volume of a pyramid is given by
[tex]\begin{gathered} Volume=\frac{1}{3}\times base\text{ }area\times altitude \\ =\frac{1}{3}\times14\times6=28\text{ cubic centimetre} \end{gathered}[/tex]Answer" 28 cubic centimetres
15) tan 330°2नउ16) tan 135°3Use the given point on the terminal side of angle to find the value of the trigonometricfunction indicated.17) tan18) sinLave(4,2√5)10,-11)
The trigonometric ratios of an angle represented with its terminal side are given by the following equations:
[tex]\begin{gathered} tanθ=\frac{y}{x} \\ sinθ=\frac{y}{\sqrt{x^2+y^2}} \end{gathered}[/tex]The first angle terminal side is located at (10, -11), then we get:
[tex]tanθ=\frac{-11}{10}=-\frac{11}{10}[/tex]Similarly, for the second angle:
[tex]\begin{gathered} sinθ=\frac{2\sqrt{5}}{\sqrt{(2\sqrt{5})^2+4^2}}=\frac{2\sqrt{5}}{\sqrt{4\times5+16}}=\frac{2\sqrt{5}}{\sqrt{20+16}}=\frac{2\sqrt{5}}{\sqrt{36}}=\frac{2}{6}\sqrt{5}=\frac{\sqrt{5}}{3} \\ sinθ=\frac{\sqrt{5}}{3} \end{gathered}[/tex]Convert the following to slop -intercept from 4x-3y=24
The slope intercept form of a line is:
[tex]y=mx+c[/tex]In this case, all we need to do is solve for y:
[tex]\begin{gathered} 4x-3y=24 \\ \end{gathered}[/tex]Let the y's be alone on one side of the equation:
[tex]4x-24=3y[/tex]Then divide both sides by 3:
[tex]\begin{gathered} y=\frac{4x-24}{3} \\ y=\frac{4}{3}x-8 \end{gathered}[/tex]Then the slope-intercept form of the line is y = 4/3x - 8
Does the following graph depict y as a function of x?
in this problem
the graph define a function, because the x-value has only one output (one value of y)
A bag has 5 blue marbles and 10 green marbles. Half of the green marbles are made of glass. A marble is selected at random from the bag. What is the probability that it is a green, glass marble
Answer:
1/3Step-by-step explanation:
Total marbles:
5 + 10 = 15Green marbles made of glass:
10/2 = 5Required probability:
P(green glass) = 5/15 = 1/3HELP ON Q1 Q2 AND Q3, WILL GIVE BRAINLIEST IF U HELP ME
The simplified expressions for each case are given as follows:
1 - a) 11g.
1 - b) 3m.
1 - c) -k².
2 - a) 8x + 11y.
2 - b) 2a + b - 2c.
3 - a) 5q + 7.
3 - b) 6r + 3s + 7t.
How to simplify an expression?An expression is simplified combining the like terms, that is, adding or subtracting, depending on the signal, the terms that have the same variable and the same exponent.
For item 1, the variables are common for all terms, hence we just add the terms keeping the variable, hence:
4g + 6g + g = 11g.4m - m = 3m.5k² - 4k² - 2k² = -k².For item 2, there are multiple variables, hence we combine the terms of each variable(we cannot add terms with x and y, for example), as follows:
5x + 3x + 5y + 6y = 8x + 11y.2a + 4b + 6c - 3b - 8c = 2a + b - 2c.Item 3 works similarly to item 2, as there are multiple variables, hence we combine the terms with each variable(or with the constant = no variable), as follows:
9q - 4q + 15 - 8 = 5q + 7.8r + 2s + 4t - 2r + s + 3t = 6r + 3s + 7t.What is the missing information?The questions are missing and are given by the image at the end of the answer.
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Can you tell me what a is and what b is and what c is
Solution
1. Reflect Across The y - axis
[tex]\begin{gathered} A^{\prime}^{\prime}(-1,-3) \\ \\ B^{\prime}^{\prime}(-5,-1) \\ \\ C^{\prime}^{\prime}(-2,-5) \end{gathered}[/tex]Using (4, 5)
[tex]\begin{gathered} A^{\prime}^{\prime}(3,2) \\ \\ B^{\prime}^{\prime}(-1,4) \\ \\ C^{\prime}^{\prime}(2,0) \end{gathered}[/tex]7 1/2 X 2 X 3
Help asap please
Answer:
Hey! So basically, 7 1/2 x 2 = 15 and 15 x 3 = 45
Hope this helped! :D
3. Jake purchased 6 packages of burgers for $53.76. Each package contains 8 burgers. How
much did Jake pay for 1 burger?
Answer:
$1.12
Step-by-step explanation:
x = 8
6x = 53.76
6(8) = 53.76
48 burgers = 53.76
Divide 53.76 by 48 for cost per burger (53.76 ÷ 48)
Please help me help me:((((((
Use synthetic division to solve (x3 + 1) ÷ (x – 1). What is the quotient?
x squared + x + 1 + StartFraction 2 Over x + 1 EndFraction
x squared minus x + 1
x squared + x + 1 + StartFraction 2 Over x minus 1 EndFraction
x cubed minus x squared + x minus 1
The quotient is equal to [tex]x^{2} +x+1[/tex]
Given
The provided equation is as follows:
[tex]\frac{x^{2}+1 }{x-1}[/tex]
What exactly is synthetic division
The synthetic division method is a quick way to divide polynomials.
When divided by the linear factor, it is also known as the polynomial division technique of a specific instance.
Therefore,
The quotient is as follows:
[tex]\frac{x^{2}+1 }{x-1}[/tex]
[tex]\frac{x(x^{2} +x+1)-1(x^{2} +x+1)}{x-1}[/tex]
[tex]\frac{(x-1)(x^{2} +x+1)}{x-1}[/tex]
[tex]x^{2} +x+1[/tex]
As a result, the quotient is
[tex]x^{2} +x+1[/tex]
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Answer: C
Step-by-step explanation:
Susan is painting her living room. Two of the walls are 10.75 feet long and 7 feet tall, and two of the walls are 6.875 feet long and 7 feet tall. If half a gallon of paint covers 200 square feet, how much paint will Susan need?
Answer:
2.63903744 gallons of paintStep-by-step explanation:
Check image below for explanation
If .5 gallon covers 200
and Susan needs 246.75
1 whole gallons covers 400 (too much)
.5 gallon = 200 paint
?? gallon = 46.75 paint
200 / 46.75 = 4.27807487
.5 / 4.27807487 = 2.13903744
2.13903744 gallon = 46.75 paint
So,
.5 gallon+ 2.13903744 gallon = 2.63903744 gallons
(200 paint + 46.75 paint = 246.75 paint)
2.6 gallons (rounded)Which of the following are geometric sequences?Check all that apply.A.2, -2, 2, -2, 2, -2, 2B.1, 2, 4, 8, 16, 32C.1, 4, 9, 16, 25, 36, 49D.10, 5, 2.5, 1.25, 0.625, 0.3125
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The correct answers are:
CONCLUSION:
The final answers are:
OPTION B and OPTION D
Can I get a tutor to help me wit this ?
we have that
The volume of a rectangular prism is given by the formula
[tex]V=L*W*H[/tex]where
V=252 cm3
H=3 cm
W=x cm
L=W+5 --------> L=x+5
substitute given values in the formula
[tex]\begin{gathered} 252=(x+5)(x)(3) \\ 252=3x^2+15x \\ 3x^2+15x=252\text{ ---> equation that models the volume} \end{gathered}[/tex]Solve the quadratic equation
using the formula
[tex]3x^2+15x-252=0[/tex]a=3
b=15
c=-252
substitute
[tex]x=\frac{-15\pm\sqrt{15^2-4(3)(-252)}}{2(3)}[/tex][tex]x=\frac{-15\pm57}{6}[/tex]The values of x are
x=7 cm and x=-12 cm ( is not a solution because is a negative number)
The width is 7 cm
therefore
Is not possible for the width to be 7.5 cm