How many feet are represented by a 4-in. line if it is drawn to ascale of 1/2 in. = 1 ft?
When working with scales, we can find the measures by using the rule of three.
From the scale, we know that 1/2 in corresponds to 1 ft, so, the rule of three is:
1/2 in --- 1ft
4 in --- x
Where "x" is the size of the line in feet repreented by the 4 in line in the drawing.
So, we cross multiply to get the equation:
[tex]\begin{gathered} \frac{1}{2}x=4\cdot1 \\ x=2\cdot4 \\ x=8 \end{gathered}[/tex]Thus, this lines represents a size of 8 ft.
Hans is a software salesman. His base salary is $1700, and he makes an additional $70 for every copy of History is Fun he sells. Let P represent his total pay (in dollars), and let N represent the number of copies of History is Fun he sells. Write an equation relating P to N. Then use this equation to find his total pay if he sells 26 coples of History Is Fun.
the equation is:
[tex]P=1700+70N[/tex]so if he sells 26 copies we get that:
[tex]P=1700+26\cdot70=3520[/tex]a square box is being cut apart and has a measurement system below. What is the surface area of the box?
ANSWER
73.5 in²
EXPLANATION
To find the surface area, we have to find the area of one face - one of the squares of the diagram - and then multiply that by 6 - because cubes have 6 faces.
The area of one face is:
[tex]A_{\text{face}}=3.5^2in^2=12.25in^2[/tex]The surface area of the box is:
[tex]\begin{gathered} S_{}=6A_{\text{face}} \\ S=6\cdot12.25in^2^{} \\ S=73.5in^2 \end{gathered}[/tex]Write the inequality that represents the sentence, "Four less than a number is greater than 49.Choose the correct answer below. A. X+4>49 -B. X-4249C. X-4> 49D. X+4> 49
Let x be the number
Thus, 4 less than a number means
[tex]x-4[/tex]4 less than a number means is greater than 49 means
[tex]x-4>49[/tex]The answer is x-4>49, option C.
Can someone please help me?
I’ll give brainliest
Answer:
161/8
Step-by-step explanation:
all the work is in the pic below sorry if I am wrong
have a nice day:)
Answer:
20 [tex]\frac{1}{8}[/tex]
Step-by-step explanation:
multiply 5 [tex]\frac{3}{4}[/tex] × 3 [tex]\frac{1}{2}[/tex] ( change to improper fractions )
= [tex]\frac{23}{4}[/tex] × [tex]\frac{7}{2}[/tex]
= [tex]\frac{23(7)}{4(2)}[/tex]
= [tex]\frac{161}{8}[/tex]
= 20 [tex]\frac{1}{8}[/tex]
An inlet pipe on a swimming pool can be used to fill the pool in 20 hours. The drain pipe can be used to empty the pool in 45 hours. If the pool is 1/3 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool?
We have the next given information:
- inlet pipe fill rate = 1/20 = 1job/hour
-The drain pipe empty rate = 1/45 job/hour
- The pool is 1/3 filled, then we need to fill 2/3.
If both are open, we have the next combined rate:
Combined rate =1/20 - 1/45 = 25/(20*45) = 25/900=1/36 = 1job/hour
Now,we need yo use the next equation:
rate * time = work done
Set x for time.
Replacing:
1/36 * x = 2/3
Multiply both sides by 36:
[tex]\begin{gathered} \frac{1}{36}*x=\frac{2}{3} \\ 36\left(\frac{1}{36}\right?x=36\ast\frac{2}{3} \\ x=24 \end{gathered}[/tex]Hence, it will take 24 hours to fill the pool
ANSWER PLEASE. FIRST ANSWER WILL BE BRAILIEST!!! DUE TODAY PLEASE HELP!!! WORTH 25 points!!!
The measure of angle C is given as follows:
<C = 80º.
Measure of angle CSegments AD and BE are parallel, hence the angles A and B are congruent, that is, they have the same measure:
<A = <B.
Angle ABE is of 50º, hence the measures of the congruent angles A and B are given as follows:
<A = <B = 50º.
The sum of the measures of the internal angles of a triangle is of 180º, hence the following relation from triangle ABC is established.
<A + <B + <C = 180º.
The measures of angles A and B were already found, hence we can solve for the measure of angle C with the above equation as follows:
<A + <B + <C = 180º.
50 + 50 + <C = 180
<C = 180 - 100
<C = 80º.
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Need help with question 2 related to literal C of question 1
For the given parabola:
Vertices, foci and asymptotes:
Vertices: (-2, 0) and (2, 0)
Foci: (-5.385, 0) and (5.385, 0)
Asymptotes: y = -(5/2)x and y = (5/2)x
Fundamental rectangle and conjugate axis endpoints:
Endpoints: 5 and -5
Use the drawing tools to form the correct answer on the provided grid. For the sequence (1,4,7, 10, ...), the index starts at 1. Graph the function f(n) on the coordinate plane, where f is a function that describes the sequence. Graph as much of the sequence as will fit on the grid.
Given
The sequence (1,4,7,10,...).
To graph the function f(n) on the coordinate plane, where f is a function that describes the sequence.
Explanation:
It is given that,
The sequence is, (1,4,7,10,...).
Since, the given sequence is an arithmetic sequence.
Then,
The first term of the sequence is 1.
The common
out of 1,000 plants, some were given a new fertilizer and the rest were given no fertilizer. Some of the plants lived and some of them died, as shown in the table above
which of the following statements is supported by the data?
A.fertilized plants died at a higher rate than unfertilized rate than unfertilozed plants did
B.fertilized plants qnd unfertilized plants died at the same rate
C. fertilized plants died at a lower rate than unfertilized plants died
D.None of the above statements can be supported by the data
The correct statement that supports the given data is; B: fertilized plants and unfertilized plants died at the same rate
How to find the death rate?Death rate is defined as the total number of deaths during a given time interval.
Now, we are given the following;
Total Number of Plants = 1000 plants
Total number of fertilized plants that lived = 200
Total number of fertilized plants that Died = 50
Total number of unfertilized plants that lived = 600
Total number of unfertilized plants that died = 150
Now, from the above it means that;
Death rate of fertilized plants = 50/250 = 0.2
Death rate of unfertilized plants = 150/750 = 0.2
Survival rate of fertilized plants = 200/250 = 0.8
Survival rate of unfertilized plants = 600/750 = 0.8
The death rates in both cases are equal
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What is the slope of a line parallel to the line whose equation is 3x-18y=-3783x−18y=−378. Fully simplify your answer.
ANSWER
Slope is 1/6
STEP-BY-STEP EXPLANATION
What to find? The slope of the line parallel to a given equation
Given equation
[tex]3x\text{ - 18y = -378}[/tex]The slope-intercept form of an equation is given below as
[tex]y\text{ = mx + b}[/tex]Where m is the slope of the line
y is the intercept of the y - axis
The next thing is to rewrite the above equation in the format of the slope-intercept equation
[tex]\begin{gathered} 3x\text{ - 18y = -378} \\ \text{ Isolate -18y by substracting 3x from both sides} \\ 3x\text{ - 3x - 18y = -378 - 3x} \\ -\text{ 18y = -3x - 378} \\ \text{Divide through by -18} \\ \frac{-18y}{-18\text{ }}\text{ = }\frac{-3x}{-18}\text{ - }\frac{378}{-18} \\ y\text{ = }\frac{1}{6}x\text{ + 21} \\ y\text{ = }\frac{1}{6}x\text{ + 21} \\ \text{ Since y = mx + b} \\ m\text{ = slope} \\ \text{Hence,m = }\frac{1}{6} \end{gathered}[/tex]For lines that are parallel to each other, the slope remains the same
[tex]m1\text{ = m2}[/tex]Therefore, the slope of the line parallel whose equation is y = 3x - 18y = -378 is 1/6
Solve 3p + 9q = 18 for q
Answer:
[tex]q=2-\frac{1}{3}p[/tex]Explanation:
Given the equation;
[tex]3p+9q=18[/tex]We want to make q the subject of formula;
firstly, let's subtract 3p from both sides;
[tex]\begin{gathered} 3p-3p+9q=18-3p \\ 9q=18-3p \end{gathered}[/tex]Then let us divide both sides by the coefficient of q;
[tex]\begin{gathered} \frac{9q}{9}=\frac{18-3p}{9} \\ q=2-\frac{1}{3}p \end{gathered}[/tex]Therefore, making q the subject of formula;
[tex]q=2-\frac{1}{3}p[/tex]the shorter leg of a right triangle is 7 m shorter than the longer leg. the hypotenuse is 7 m longer than the longer leg. find the side lengths of the triangle. length of the shorter leg:length of the longer leg:length of the hypotenuse:
Answer:
Explanation:
Let the length of the longer leg = x m
The shorter leg of a right triangle is 7m shorter than the longer leg. therefore:
Length of the shorter leg = (x-7) m
The hypotenuse is 7m longer than the longer leg.
Length of the hypotenuse = (x+7) m
We solve for x using Pythagoras Theorem.
[tex]\text{Hypotenuse}^2=\text{Opposite}^2+\text{Adjacent}^2^{}[/tex]This gives us:
[tex]\begin{gathered} (x+7)^2=x^2+(x-7)^2 \\ (x+7)(x+7)=x^2+(x-7)(x-7) \\ x^2+14x+49=x^2+x^2-14x+49 \\ 2x^2-x^2-14x-14x-49+49=0 \\ x^2-28x=0 \\ x(x-28)=0 \\ x-28=0\text{ or x=0} \\ x=28\text{ meters} \end{gathered}[/tex]Therefore:
• Length of the shorter leg: 28-7 = 21 meters
,• Length of the longer leg: 28 meters
,• Length of the hypotenuse: 28+7 = 35 meters
1.Arsenic-74 is used to locate brain tumors. It has a half-life of 17.5 days. 90 mg wereused in a procedure. Write an equation that can be used to determine how much ofthe isotope is left after x number of half-lives.2. how much would be left after 70 days ?
2) 5.625 mg will be left
Explanation:1) Half-life = 17.5 days
initial amount of Arsenic-74 = 90 mg
To get the equation, we will use the equation of half-life:
[tex]\begin{gathered} N_t\text{ = N}_0(\frac{1}{2})^{\frac{t}{t_{\frac{1}{2}}}} \\ where\text{ N}_t\text{ = amount remaining} \\ N_0\text{ = initial amount} \\ t_{\frac{1}{2}\text{ }}\text{ = half-life} \end{gathered}[/tex][tex]N_t\text{ = 90\lparen}\frac{1}{2})^{\frac{t}{17.5}}[/tex]2) we need to find the remaining amount of Arsenic-74 after 70 days
t = 70
[tex]\begin{gathered} N_t=\text{ 90\lparen}\frac{1}{2})^{\frac{70}{17.5}} \\ N_t\text{ = 5.625 mg} \end{gathered}[/tex]So after 70 days, 5.625 mg will be left
a.Convert 7/9 to a percent and decimal.b.Write these numbers from least to greatest: 6/8, 7/8, 7/9
a. To convert the number 7/9 to a decimal we need to solve the division:
[tex]\frac{7}{9}=0.778[/tex]Thus, 7/9 as a decimal number is 0.778.
To convert it to a percent, multiply the decimal form by 100%:
[tex]0.778\cdot100=77.8\text{ \%}[/tex]b. To write the numbers from least to greatest we need to convert these fractions to the same denominator, we can do it by multiplying the fractions 6/8 and 7/8 by 9/9 and the fraction 7/9 by 8/8, as follows:
[tex]\begin{gathered} \frac{6}{8}\cdot\frac{9}{9}=\frac{54}{72} \\ \frac{7}{8}\cdot\frac{9}{9}=\frac{63}{72} \\ \frac{7}{9}\cdot\frac{8}{8}=\frac{56}{72} \end{gathered}[/tex]Thus, in order from least to greatest it is: 54/72 , 56/72 , 63/72.
This order corresponds to:
6/8 , 7/9 , 7/8
Simplify (c3d2)4.
cd24
c12d8
c7d12
c7d6
By algebra properties, the simplified form of (c³ · d²)⁴ is equal to c¹² · d⁸. (Correct choice: B)
How to simplify an algebraic expression
In this problem we find the power of the product of two powers whose variables are c and d and which must be simplified by using algebra properties. The complete procedure is shown below:
(c³ · d²)⁴ Given(c³)⁴ · (d²)⁴ Power of a productc¹² · d⁸ Power of a power / Definition of multiplication / ResultThe simplified form of the algebraic expression is c¹² · d⁸.
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In the Alaskan temperature data set, what is the outlier, if any?5, 12, 14, 19, 19, 21, 25, 29, 33
ANSWER
5
EXPLANATION
We want to find the outlier in the data set given.
An outlier is a data point whose value is abnormal or incoherent with other values in the same data set.
That means that it's value does not tally with the other values in measure.
Therefore, the outlier from the data set is 5.
3. What should be done first to simplify: 16 - 8 • 4 8.2
In that case we must perform the division (16÷8) before multiplication as the rules says that we must work from left to right in case of only having multiplications and divisions.
So the answer is the first option.
What are the 2 right angle measures? * 40 and 120 120 and 60 180 and 120 140 and 40
The two right angle measure is 120° and 60° and 140° and 40° .
In mathematics and trigonometry, a right angle is a quarter-turn or an angle that is exactly 90 degrees or π/2 radians . If a ray is positioned so that its terminal is in a line and they are equal, the adjacent angles represent right angles.
Orthogonality, which refers to the property of producing right angles, and perpendicular lines, which are defined as lines that intersect at right angles, are important and closely related geometrical concepts.
The existence of a feature resembling a right angle, which distinguishes right triangles, makes all right angles a fundamental notion in trigonometry.
We know that a right angle is equal to 90° .
Hence 2 right angles = 90° × 2 = 180°
Now we will use the options to check if they add up to 2 right angles or 180°
120° + 60° = 180°
140° + 40° = 180°
Therefore they are he required options that satisfy the given condition.
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A. Solve for y.
y = ______
B. Find the measure of angles A, C and D showing all work.
∠A = _______, ∠C = ________, ∠D = ________
A and B are Vertical Angles and are thus congruent.
A = B
3y - 24 = 51
3y - 24 + 24 = 51 + 24
3y = 75
3y/3 = 75/3
y = 25
We can solve for A, but we already know A = B and B = 51, so A = 51.
C and D are also Vertical Angles. Since these angles go all the way around, they add up to 360.
51 + 51 + C + D = 360
C = D
C = x
D = x
D + C = 2x
102 + 2x = 360
102 - 102 + 2x = 360 - 102
2x = 258
2x/2 = 258/2
x = 129
C = 129
D = 129
For triangle ABC, ∡c=90°. Draw and label a diagram for this triangle, then find the measures of the remaining angles and sides. Explain how you found each measure.
Given:-
[tex]\Delta ABC,\angle C=90[/tex]To find:-
Draw and label a diagram for this triangle, then find the measures of the remaining angles and sides. Explain how you found each measure.
At first construct an right angled triangle at c. so we get,
So now we need to use a protractor and measure the angle A and angle B.
Graph JKL and its image after a reflection in the line x=-1
J(2,-1)
K (4,-5)
L (3,1)
The image after a reflection in the line x = -1 exists J(2, -1), K (4, -5) and L (3, 1) then of the reflection exists J' = (2, -1), K' = (4, -5) and L' = (3, 1).
What is meant by reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure exists said to reflect the other figure when they exists all equally spaced apart from one another.
When a shape exists reflected, it must be reflected across a line.
The coordinates are given as:
J(2,-1), K (4,-5) and L (3,1)
The rule of reflection across the y-axis exists:
(x, y) [tex]$\rightarrow[/tex](-x, y)
So, the image of the reflection exists:
J' = (2, -1)
K' = (4, -5)
L' = (3, 1)
Therefore, the reflection exists J' = (2, -1), K' = (4, -5) and L' = (3, 1).
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Question 35?Find the indicated function and state its domain in interval notation?
Question 35.
Given:
[tex]\begin{gathered} f(x)=x-5 \\ \\ g(x)=\sqrt[]{x+3} \\ \\ \text{Let's solve for }\frac{f(x)}{g(x)} \end{gathered}[/tex]To solve the function operation, let's divide both functions.
Hence, we have:
[tex]\frac{f(x)}{g(x)}=\frac{x-5}{\sqrt[]{x+3}}[/tex]Now, let's find the domain of the function f(x)/g(x).
Domain is the set of all possible x-values that makes the function true.
Hence, to find the domain, set the expression in the radicand equal to zero.
We have:
x + 3 = 0
Subtract 3 fromboth sides:
x + 3 - 3 = 0 - 3
x = - 3
Therefore, the domain in interval notation is:
(-3, ∞).
ANSWER:
[tex]\begin{gathered} \frac{h(x)}{g(x)}=\frac{x-5}{\sqrt[]{x+3}} \\ \\ \text{Domain:}(-3,\infty) \end{gathered}[/tex]
What is the gcf of 12 and 86?
factors of 12: 1, 2, 3, 4, 6, 12
factors of 86: 1, 2, 43, 86
Then, the greatest common factor (gcf) is 2
Solve the system by elimination. x+y=2x-y=6
ANSWER:
x = 4 and y = -2
STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} x+y=2 \\ x-y=6 \end{gathered}[/tex]To use the elimination system, we only have to add both equations, like this:
[tex]\begin{gathered} x+y+x-y=2+6 \\ 2x=8 \\ x=\frac{8}{2} \\ x=4 \\ \\ \text{ now, for y:} \\ x+y=2 \\ 4+y=2 \\ y=2-4 \\ y=-2 \end{gathered}[/tex]The value of x is 4 and the value of y is -2
In the formula C = pmn, p stands for___
A. price per item
B. period
C. promotion
D. percent
Below are the times (in days) it takes for a sample of 5 customers from Tony's computer store to pay their invoices.
In this problem, we have the following data sample:
[tex]32,37,24,22,20.[/tex]We must compute the standard deviation of this data sample.
1) First, we compute the mean value which is given by the following formula:
[tex]\bar{x}=\frac{\sum^n_{i\mathop=1}x_i}{n}=\frac{32+37+24+22+20}{5}=\frac{135}{5}=27.[/tex]2) Now, we compute the standard deviation using the following formula:
[tex]\sigma=\sqrt[]{\frac{\sum^n_{i\mathop{=}1}(x_i-\bar{x})^2}{n-1}}=\sqrt[]{\frac{208}{5-1}}\cong7.21.[/tex]Answer
The standard deviation is 7.21.
Solve.
Separate your answers with a comma, and please write fractions in reduced form, no decimals.
8|6x−6|=24
The value of x in reduced fraction form is 3/2.
A fraction is a value written in the form of a quotient which has an upper number called numerator and lower called denominator. It represents a part of a whole.
8|6x−6|=24 (given equation)
|6x-6| = 24/8
|6x-6| = 3
6x = 3+6
6x = 9
x = 9/6 ( To reduce divide both the terms with 3 that is a common factor)
x = 3/2
Therefore, we can conclude that the value of x in reduced fraction is 3/2.
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Please need help fast!
Answer:
Slope is [tex]-\frac{7}{2}[/tex] and the y-intercept is (0,-2)
Step-by-step explanation:
First, turn the equation into slope-intercept form.
Slope intercept form is [tex]y=mx+b[/tex]. Where m is the slope and b is the y-intercept
The equation would be [tex]y=\frac{4-7x}{-2}[/tex]. Which is equal to [tex]y=\frac{-7}{2} x-2[/tex].
This means that the slope would be [tex]-\frac{7}{2}[/tex] and the y-intercept is (0,-2)
Josiah can jog 5/6 mile in 15 min find his average speed in miles per hour
Answer:
3 1/3 miles per hourStep-by-step explanation:
Given speed:
5/6 mile per 15 minConvert this to mph as follows:
5/6 mile per 15*1/60 h, since 1 min = 1/60 h5/6 mile per 1/4 h, simplify5/6 : 1/4 mile per 1/4 : 1/4 h, divide both sides by 1/45/6 *4 mile per 1 h, multiply10/3 mile per hour, 3 1/3 miles per hour, convert to mixed fractionAnswer:
10/3 miles per hour
Step-by-step explanation:
Given that,
→ 5/6 mile in 15 min
→ 15 min × 4 = 1 hour
Average speed in miles per hour,
→ 5/6 × 4
→ 20/6
→ 10/3 miles per hour
Hence, required answer is 10/3.
