ANSWER
50,000 + 100x = 75,000
STEP-BY-STEP EXPLANATION:
Given parameters
• Ed base salary = $50, 000
,• Commission on each computer sells = $100
,• Total income = $75,000
Let x be the number of computers sold
Total income = base salary + commission * number of cars sold
75000 = 50000 + 100* x
50,000 + 100x = 75, 000
Hence, the equation that can be used to find the number of cars sold is
50,000 + 100x = 75,000
Which of the following is not a step in solving the equation 3/x = 8/7 (1) Divide both sides of the equation by 8(2) Use cross products to write the equation 3.7 =8x(3) Divide both sides of the equation by 3(4) Rewrite 3.7 as 21
Let's solve the equation:
3/x = 8/7
8x = 3 * 7 Cross product
8x = 21 Rewrite 3 * 7 as 21
Dividing both sides by 8:
8x/8 = 21/8
x = 2.625
As you can see, we do not follow step 3. Divide both sides of the equation by 3.
10 ex 9 10 ex 3 simplified
ANSWER
[tex]10^6[/tex]EXPLANATION
We want to simplify the fraction below:
[tex]\frac{10^9}{10^3}[/tex]When you have a fraction of powers and the numerator and denominator have the same base (e.g. 10 in this case), the power on the denominator is subtracted from the power of the numerator.
So, that is:
[tex]\begin{gathered} 10^{9-\text{ 3}} \\ =>10^6 \end{gathered}[/tex]That is the answer.
Find the value of 4² + 6².
Answer:
Step-by-step explanation:
52
Answer: The correct answer is 52
Step-by-step explanation:
4² + 6²
4*4 + 6*6
16 + 36 = 52
Can anyone help me with this a 7 more problem
We are given the following statement.
If a number is an integer, then it is either positve or negative.
In the above statement, the 1st part is the condition and the 2nd part is conclusion.
Condition = a number is an integer
Conclusion = it is either positve or negative
Therefore, the conclusion of the conditional is option B.
A number is either positive or negative.
An arch is in the shape of a parabola. It has a span of 96 feet and a maximum height of 8 feet.Find the equation of the parabola. ______________Determine the distance from the center at which the height is 2 feet. ___________
We know the equation of a parabola can be written as
y = a(x-b1) (x-b2) where a is a constant and b1 and b2 are the zeros
y = a ( x - 48) ( x - -48)
y = a ( x-48) (x+48)
Now when x = 0 y = 8
8 = a ( 0-48) ( 0+48)
8 = a (-2304)
-8/2304 = a
-1/288 = a
y = -1/288 ( x-48) (x+48)
This is the equation for the parabola
Now let y = 2
2 = -1/288 ( x-48) (x+48)
Multiply each side by -288
-576 = (x-48)(x+48)
FOIL
-576 = x^2- 2304
ADD 2304 to each side
1728=x^2
Take the square root of each side
24 sqrt(3) = x
24 sqrt(3) ft
41.569 ft
A Scientist uses 10 grams of carbon evrey 15 mins during an experiment. If the experiment lasted 3 hours, how many total kilograms of carbon did they use
We know that
• A scientist uses 10 grams every 15 minutes.
To find the kilograms used in 3 hours, first, we transform 10 grams into kilograms
[tex]\frac{10}{1000}kg=0.01\operatorname{kg}[/tex]Then, we use the following proportion
[tex]\frac{0.01\operatorname{kg}}{x}=\frac{15\min }{180\min }[/tex]Because 3 hours is equivalent to 180 minutes. Let's solve for x
[tex]\begin{gathered} x=\frac{180\cdot0.01}{15} \\ x=0.12 \end{gathered}[/tex]Hence, the total kilograms are 0.12.I would like someone to help me so I can understand what to do. Pls anyone
we have that
2 cups in a pint
2 pints in a quart
4 quarts in a gallon
so
4 cups in 2 pints
4 cups in a quart
16 cups in 4 quarts
16 cups in a gallon
and
we have
3 parts red and 5 parts yellow
3 parts +5 parts=8 parts
8 parts=1 gallon
red paint fraction is 3/8 gallon
yellow paint fraction is 5/8 gallon
Remember that
I need 16 cups for a gallon
Apply proportion
16/1=x/(3/8)
x=(3/8)16
x=6 cupsSuppose a sample of 383 Americans over 21 is drawn. Of these people, 280 don't smoke. Using the data, construct the 80% confidence interval for the population proportion of Americans over 21 who smoke. Round your answers to three decimal places.
The 80% confidence interval for the population proportion of Americans over 21 who smoke is: 0.240; 0.298.
How to find the confidence interval?First step is to find the population proportion p
Sample size = n = 383
Using this formula to find the population proportion (p)
p = x /n
Let plug in the formula
p = (383 - 280) / 383
p = 103/383
p = 0.2689
Second step is to find the Margin of error (MOE)
Value of z-score for a confidence level of 80%= 1.282
Using this formula to margin of error
MOE =( z alpha x √(p) (1-p) / n )
Let plug in the formula
MOE =( 1.282x √(0.2689)(1-.0.2689) / 383)
MOE =( 1.282 x √(0.2689)(0.7311) / 383)
MOE =( 1.282 x √0.000513297
MOE =( 1.282 x 0.0226561)
MOE = 0.02905
Third step is to find the confidence interval (CI)
Confidence interval = p ± MOE
Confidence interval = 0.2689 ± 0.02905
Confidence interval = ( 0.2689 - 0.02905) , (0.57 + 0.02905)
Confidence interval = 0.23985; 0.29795
Confidence interval = 0.240; 0.298 ( Three decimal places)
Therefore the CI is 0.240; 0.298.
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Find the product 54,612 x 46?
Explanation
Step 1
Multiply. as you would with whole numbers.( ignore the comma)
so
[tex]\begin{gathered} 54,612x46\rightarrow54612\cdot46=2512152 \\ \end{gathered}[/tex]Step 2
Count the total number of decimal places in your factors.
[tex]54,612\rightarrow\text{3 numbers in decimal places}[/tex]Step 3
Move the decimal point in the product one place to the left for each decimal place you counted.
so
[tex]2512152\rightarrow3\text{ places}\rightarrow2512,152[/tex]so, the answer is
[tex]2512,152[/tex]I hope this helps you
Solve 9abs(3n-2) + 6 > 51 and graph on the number line
Solving the inequality,
[tex]\begin{gathered} 9\lvert3n-2\rvert+6>51 \\ \rightarrow9\lvert3n-2\rvert>45 \\ \rightarrow\lvert3n-2\rvert>5 \end{gathered}[/tex]Remember that if
[tex]\lvert u\rvert>a,a>0\Rightarrow u<-a\text{ or }u>a[/tex]This way, we get:
[tex]\begin{gathered} 3n-2<-5\rightarrow3n<-3\rightarrow n<-1 \\ 3n-2>5\rightarrow3n>7\rightarrow n>\frac{7}{3} \end{gathered}[/tex]As an interval, we get:
[tex]\: \mleft(-\infty\: ,\: -1\mright)\cup\mleft(\frac{7}{3},\: \infty\: \mright)[/tex]In the number line, we get:
Question 3(Multiple Choice Worth 3 points)
(01.02 MC)
Joaquin wants to make his famous chocolate chip cookies to bring to his friend's birthday party. The original recipe serves 5 people and requires 1/4 a cup of butter but he needs to serve 28 people. How many cups of butter will he need?
Answer:
B
Step-by-step explanation:
Complete the following statements.
In general, ________% of the values in a data set lie at or below the median.
________% of the values in a data set lie at or below the third quartile (Q3).
If a sample consists of 2100 test scores, ________ of them would be at or below the second quartile (Q2).
If a sample consists of 2100 test scores, ________ of them would be at or above the first quartile (Q1).
In general, 50% of the values in a data set lie at or below the median.
75% of the values in a data set lie at or below the third quartile (Q3).
If a sample consists of 2100 test scores, 1100 of them would be at or below the second quartile (Q2).
If a sample consists of 2100 test scores, 525 of them would be at or above the first quartile (Q1).
What are quartiles?Three values called quartiles divide sorted data into four equal portions with the same amount of observations in each.
One kind of quantile is a quantile. Q1, or the lower quartile, is another name for the first quartile.
Second quartile: Also referred to as the median or Q2.
Third quartile, or the upper quartile, is also referred to as Q3.
The second quartile is 50%
Samples of 2100 test scores that are at or below at the second quartile
= 50% of 2100
= 0.5 * 2100
= 1100
The first quartile is 25%
= 0.25 * 2100
= 525
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20 points 2. Krisstopher was driving to Houston from Pasadena, he drives a 2 3/4 miles and stops for a break. He then drives 5 1/2 miles to reach his destination. What distance in miles did Krisstopher travel to reach his final destination. 81/4 miles 71/2 miles 81/2 miles 6 1/3 miles Clear selection
Add 2 + 3/4 + 5 + 1/2
this gives (2+5) + ( 3/4+2/4)
7 + 5/4 = 8.25
on square PQRS below, if Q is located at (7, 0) and R is located at (5, -8), what is the length of SRleave it in radical form
In a square, all the sides are the same length.
[tex]PQ=QR=SR=SP[/tex]So, to find the length of the segment SR you can find the length of the segment QR using the formula of the distance between two points, that is:
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2^{}} \\ \text{ Where d is the distance between two points } \\ A(x_1,y_1)\text{ and} \\ B(x_2,y_2) \end{gathered}[/tex]So, in this case, you have
[tex]\begin{gathered} Q(7,0) \\ R(5,-8) \\ d=\sqrt[]{(5_{}-7)^2+(-8-0)^2} \\ d=\sqrt[]{(-2)^2+(-8)^2} \\ d=\sqrt[]{4+64} \\ d=\sqrt[]{68} \end{gathered}[/tex]Therefore, the length of the segment SR is
[tex]\sqrt[]{68}[/tex]If h(x)=-3x and g(x)=2x-1 what input value would make h(x)=12?
The question gives the function h(x) as
[tex]h(x)=-3x[/tex]To find the value that will make the function 12, we equate the function to 12, such that
[tex]-3x=12[/tex]Solving to get x, we have
[tex]\begin{gathered} x=\frac{12}{-3} \\ x=4 \end{gathered}[/tex]Therefore, h(x) = 12 when x = 4.
You have a bag of 36 ounces of popcorn. Your friend eats 1/4 of the bag. You eat 1/3 of the bag. How many ounces did you eat? How many ounces are left?
Answer: You Eat: 12 ounces. There are 15 ounces left.
Step-by-step explanation:
36(1/4)=9 ounces
36(1/3)=12 ounces, which is how much you eat.
36-12-9=15 ounces left
Step-by-step explanation:
How many ounces did you eat?
¼+⅓=3+4/12=7/12 ounces were eaten
How many ounces are left?
36-7/12=432-7/12
=425/12
=\frac{425}{12}
=35^5/12
find the percent notation for 0.376
To convert a decimal into a percentage we have to multiply the decimal by 100, as follows:
[tex]0.376\cdot100=37.6\text{ \%}[/tex]0.376 is equivalent to 37.6 %
What is the parallel slope to this equation? f(x)=-5x + 6
Remember the equation of a line with slope m and y-intercept b:
[tex]y=mx+b[/tex]Which can be expressed in terms of functions by replacing y=f(x)
[tex]f(x)=mx+b[/tex]Any line with the same slope will be parallel to that equation.
By comparing with:
[tex]f(x)=-5x+6[/tex]We can know that its slope is equal to -5.
Since the "parallel slope" is just the slope, then
Joy has $68,020 in a savings account that earns 13% annually. The interest is not compounded. How much will she have in 5 years?
A = P + I
A is the new value
P is the initial value
I is the interest
I = PRT
R is the rate in decimal
T is the time
Joy has $68020
P = 68020
The account earns 13% annually
R = 13% = 13/100 = 0.13
The time is 5 years
T = 5
Let us find I, then A
I = 68020(0.13)(5)
I = 44213
Now let us find A
A = 68020 + 44213
A = $112233
She has $112233 in 5 years
which choices are equivalent to the expression below? check all that apply.[tex] 4\sqrt{6} [/tex]a. [tex] \sqrt{96} [/tex]b.[tex] \sqrt{24} [/tex]c. 96d. [tex] \sqrt{4} \times \sqrt{36} [/tex]e.[tex] \sqrt{16} \times \sqrt{6} [/tex]f.[tex] \sqrt{32} \times \sqrt{3} [/tex]
To find the equivalents of this expression we can write it another way:
[tex]4\cdot\sqrt[]{6}=\sqrt[]{16\cdot6}=\sqrt[]{4\cdot4\cdot6}=\sqrt[]{2\cdot2\cdot2\cdot2\cdot2\cdot3}[/tex]We can group the 2's and 3 however we want and the expression will be the same.
If we do the multiplication of all of them (or 16 times 6, is the same) we get that it's 96, so option a is one equivalent
[tex]\sqrt[]{96}[/tex]Then from the second term we have that another equivalent is
[tex]\sqrt[]{16}\cdot\sqrt[]{6}[/tex]Because the square root can be distributed into the product. So option e is equivalent
If we multiply all the 2's we get that it's 32, so another equivalent is:
[tex]\sqrt[]{32}\cdot\sqrt[]{3}[/tex]Option f is equivalent
A triangle has vertices on a coordinate grid at D(-5, -2), E(-5,4), andF(-1,4). What is the length, in units, of DE?
To find the length of DE,
Here D = (-5,-2) and E = (-5,4).
Hence the distance is given by
[tex]DE=\sqrt[]{(-5+5)^2+(4+2)^2}[/tex]On simplifying,
[tex]\begin{gathered} DE=\sqrt[]{6^2} \\ DE=6 \end{gathered}[/tex]Hence the length of DE is 6 units
write an equivalent ratio in simplest form of the ratio 1852 to 3690
926/1845
Explanation:To get the equivalent ratio in its simplest form, wefind the numbers common to both numbers.
[tex]\begin{gathered} \frac{1852}{3690} \\ \end{gathered}[/tex]2 is common to both, so we divide:
[tex]\begin{gathered} 1852\div\text{ 2 = 926 } \\ 3690\div2\text{ = 1845} \\ \frac{926}{1845} \end{gathered}[/tex]We check again if there is a number common to them
No number is common to both numerator and denominator asides 1
Hence, the simplest form is 926/1845
Last week you worked 28 hours, and earned $266. What is your hourly pay rate? $ per hour Give your answer in dollars and cents (like 5.50)
1) Gathering the data
Last week
28 worked hours = $266
What is your hourly pay rate?
2) To find out that, let's set a proportion
Worked hours $
28------------------------ 266
1--------------------------- x
Let's use the fundamental property of a proportion that allows us to cross multiply the ratios of that proportion
So the hourly pay rate is approximately $11.08 per hour.
Find the circumference of the circle. Round to the nearest hundredth if necessary. (Use 3.14 for a) A circle with a diameter of 18 in
Given data:
The given diameter of the circle is D=18 in.
The expression for the circumference is,
[tex]C=\pi D[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} C=\pi(18\text{ in)} \\ =56.52\text{ in} \end{gathered}[/tex]Thus, the circumference of the circle is 56.52 in.
The circumference of the hub cap of a tire is 79.63 centimeters. Find the area of this hub cap. Us3.14 for a. Use pencil and paper. If the circumference of the hub cap were smaller, explain how twould change the area of the hub cap.The area of this hub cap is about square centimeters.(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearestthousandth as needed.)
Recall that the circumference of a circle is given by the following formula:
[tex]C=2\pi r,[/tex]where r is the radius of the circle.
We are given that:
[tex]79.63cm=2\pi r,[/tex]therefore:
[tex]r=\frac{79.63}{2*\pi}cm.[/tex]Now, the area of a circle is given by the following formula:
[tex]A=\pi r^2,[/tex]Therefore, the area of the hub cap is:
[tex]A=\pi *(\frac{79.63cm}{2})^2*\frac{1}{\pi^2}\approx505cm^2.[/tex]Answer:
[tex]\begin{equation*} 505cm^2. \end{equation*}[/tex]Given that the radius of the circle and the circumference are proportionally related, if the circumference is smaller then the radius is smaller. The area is proportionally related to the radius squared, therefore, a smaller circumference implies a smaller radius which implies a smaller area.
Which value is in the solution for the inequality 7 + 3x < 37?
the solution of the inequality will be x<10, i mean all the real numbers that are less than 10. It's because:
[tex]7+3x<37\Rightarrow3x<37-7=30\Rightarrow x<\frac{30}{3}=10[/tex]What is the equation of the line shiwn graphed below
we are given the horizontal line. To determine the equation of this line let's remember that the equation of any horizontal line is of the form:
[tex]y=k[/tex]Where "k" is the point where the line touches the y-axis, in this case, the equation of the line is:
[tex]y=4[/tex]2) Find the volume of a shoe box that is wide9, 15 inches, and 6 inches high.
volume of the shoe box is 1080 inches³
Explanation:2) The shoe box is rectangular prism
So we will find the volume of a rectangular prism:
Volume of rectangular prism = length × width × height
length = 15 inches
width = 9 inches
height = 6 inches
Volume = 15 × 9 ×6
Volume = 1080 inches³
Hence, the volume of the shoe box is 1080 inches³
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 34minutes of calls is $25.92, and the remaining credit after 53 minutes of calls is $23.64. What is the remaining credit after 71 minutes of calls?
The remaining credit after 71 minutes is $21.48
To solve this, we can calculate the equation of the linear function that represents the remaining credit
x is the time in minutes, y is the remaining credit. the we have two points of the line and we can calculate the equation
34 min and $25.92 => (34,25.92)
53 min and 23.64 => (53,23.64)
the formula to calculate the slope of a line is
[tex]m=\frac{y_2-y_1}{x_2-x_1_{}}=\frac{23.64-25.92}{53-34}=-0.12[/tex]now we know the slope, we can get the line euqation
[tex]y=m(x-x_1)+y_1\Rightarrow\text{ y=-0.12(x-34)+25.92=-0.12x+30}[/tex]Now for wathever x we ask, just plug it in to the equation and will give you the reamining credit.
for x=71 min:
[tex]y=-0.12(71)+30=-8.52+30=21.48[/tex]theremaining credit is $21.48.
Dan paid three times as much as Greg for his dinner. (Translate the given situation into an equation. Pick the variable you use according to the context.
Let d represent Dan payment and let g represent Greg payment
"Dan paid three times as much as Greg for his dinner" can be represented as
d= 3g
Number 2
Let x represent the cost of Gym A and Y represent the cost of Gym B
Since Gym B cost twice as much as Gym A
Then y=2x
Number 3
Let d represent Diana's race and let c represent Calorine's race
Diana = 3 x Calorine
d=3c