1) Variables:
D: distance away from the surface
T: temperature
2) the b-value of the y-intercept for your equation is 15, because it's the surface temperature, that is, at D = 0, T = 15
4) the slope is: -6.5, because temperature decreases approximately 6.5 degrees Celsius for each kilometer traveled away from the surface
5) Equation:
T = -6.5D + 15
How do you solve this equation? K-10/2=-7
Given the following equation:
[tex]K-\frac{10}{2}=-7[/tex]We know that:
[tex]\frac{10}{2}=5[/tex]Then:
[tex]K-5=-7[/tex]Now, we add 5 on both sides:
[tex]\begin{gathered} K-5+5=-7+5 \\ \Rightarrow K=-2 \end{gathered}[/tex]AEHS – Algebra – Review Solve the following problems: 1. Evaluate: X2 + 5X-8 For X = 2 2. Evaluate: 5X + 2y for x = 4, y = 3 3. Solve: X + 7 = 20 4. Solve: 6X = 30 5. Solve: 2X – 5 = 7 6. X/2 + 1 = 6. 7. 3m+4=25 8. |X-4|=10 9. Fine the mean, Median, Mode and Range of 6, 7, 3, 8, 13, 3, 9 10. Fine the sale price if the original price is $150 and Mark up 60%. 11. Fine the sale price if the original price is $90 and discount is 20%. 12. Fine the total cost if the original price is $120 and sale tax is 7%.
Question 1
[tex]\text{Evaluate x}^2\text{ + 5x - 8 for x = 2}[/tex]Substitute x in the expression
[tex]\begin{gathered} =2^2\text{ + 5 }\times\text{ 2 - 8} \\ =4\text{ + 10 - 8} \\ =14\text{ - 8} \\ =6 \end{gathered}[/tex]This is from my ACT prep guide workbookI am a beginner at this kind of math If you can, please explain step-by-step thoroughly on how to answer this problem :) thank you in advance
ANSWER
J. 63
EXPLANATION
We know that x is a positive integer and the other expression is also a positive integer. First, simplify the expression by taking x as a common factor,
[tex]\frac{x}{3}+\frac{x}{7}+\frac{x}{9}=x(\frac{1}{3}+\frac{1}{7}+\frac{1}{9})[/tex]Then, add the coefficients. First, we have to find the least common denominator. 9 is a multiple of 3, and 7 is a primal number, thus the least common denominator is 9x7 = 63,
[tex]x(\frac{1}{3}+\frac{1}{7}+\frac{1}{9})=x\frac{21+9+7}{63}=x\cdot\frac{37}{63}[/tex]37 and 63 have no common factors, so that fraction cannot be simplified. As we can see there is a fraction multiplying x, but we were told that the expression was a positive integer, so we have to find x so that this expression results in an integer. Also, x must be an integer too. The least value of x is the one that cancels out the denominator of the fraction,
[tex]x\cdot\frac{37}{63}=63\cdot\frac{37}{63}=37[/tex]Hence, the least value of x is 63
I need help with this question, please. This is non graded.
Given:
Given that a rectangular prism with
[tex]\begin{gathered} l=2x-3 \\ w=x+1 \\ h=3x+4 \end{gathered}[/tex]Required:
To find the volume of the rectangular prism.
Explanation:
The formula for volume of the rectangular prism is
[tex]V=l\times w\times h[/tex]Now
[tex]undefined[/tex]Please help me to solve this question. It is not from a test. Thank you for helping me if you do :)The first options are: 0.57, 0.73. Second, 0.74, 0.57. Third: no, yes. Fourth (bottom) : much greater than or close to
Answer:
• 0.73
,• 0.57
,• Yes
,• Much greater than
Explanation:
The completed table is attached below:
(a) P(improvement| medicine)
[tex]P(improvement|medicine)=\frac{63}{86}\approx0.73[/tex](b)P(improvement)
[tex]P\left(improvement\right)=\frac{85}{150}\approx0.57[/tex](c)
Yes, there is evidence that a patient who takes the medicine is more likely to show improvement than a randomly chosen patient from the group because P(improvement |took medicine) is much greater than P(improvement).
The equation y=3x-6 and the table describe twi different linear functions Which function had the greatest rate of change? Explain
The rate of change is measured by the slope m.
In case of y=3x-6, the slope is the coefficient of x, that is, the slope m is
[tex]m=3[/tex]Now, in the case of the table, we must find the slope m by choosing two points. The slope formula in this case is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where we chose:
[tex]\begin{gathered} (x_1,y_1)=(2,9) \\ (x_2,y_2)=(4,16) \end{gathered}[/tex]Then, by substituting these values into the slope formula, we have
[tex]\begin{gathered} m=\frac{16-9}{4-2} \\ m=\frac{7}{2} \\ m=3.5 \end{gathered}[/tex]By comparing the slopes, we can see that the function represented in the table has the greatest rate of chance because 3.5>3
Rashid left a $17 tip for a $85 restaurant bill. What percent tip did he leave
Answer:
[tex]20\text{ \%}[/tex]Explanation:
Here, we want to get the percentage of the tip left
Mathematically, we have to divide the tip by the bill and multiply by 100%
We have that as:
[tex]\frac{17}{85}\times\text{ 100 \% = 20\%}[/tex]You just scored 40 correct I have a possible 50 on your Health information test. what percentage did you earn?
This is:
[tex]\frac{40}{50}\times100\%[/tex]Solve:
[tex]0.8\times100\%=80\%[/tex]Answer: 80%
what is the solution of each system ? use elimination 5x-6y=-32-3x-3y=9
Answer:
x = -50/11
y = 17/11
Explanation:
We have the following system of equations:
5x - 6y = -32
-3x - 3y = 9
To solve by elimination, we will multiply both sides of the second equation by -2, so:
[tex]\begin{gathered} -2(-3x-3y)=-2(9) \\ -2(-3x)-2(-3y)=-18 \\ 6x+6y=-18 \end{gathered}[/tex]Now, we can add this equation with the first equation, so:
5x - 6x = -32
6x + 6x = -18
11x + 0 = -50
So, solving for x, we get:
11x = - 50
11x/11 = -50/11
x = -50/11
Then, we can replace the value of x by -50/11 on the first equation:
[tex]\begin{gathered} 5x-6y=-32 \\ 5(-\frac{50}{11})-6y=-32 \end{gathered}[/tex]So, solving for y, we get:
[tex]\begin{gathered} -\frac{250}{11}-6y=-32 \\ -\frac{250}{11}-6y+\frac{250}{11}=-32+\frac{250}{11} \\ -6y=-\frac{102}{11} \\ \frac{-6y}{-6}=\frac{-102}{11}\cdot\frac{1}{-6} \\ y=\frac{17}{11} \end{gathered}[/tex]Therefore, the solution of the system is:
x = -50/11
y = 17/11
Holly has $10.00. she saw a purse onna catalog wlthat was marked $14.96 plus 5% sales tax.How much more money does Holly need to buy the purse.A. $5.70B.$5.00C.$9.95D.$5.95E.$5.45
First, we find the price including the sales tax. First, we find the sales tax amount
[tex]14.96\cdot0.05=0.75[/tex]Then, we add
[tex]14.96+0.75=15.70[/tex]Now, we subtract from the money Holly has
[tex]10-15.70=-5.70[/tex]Hence, the answer is A. $5.70.craig has £2700 in the bank. it earns 3.5 percent interest annully. How much will the account after 5 years?
Craig has$2700 in the bank. The amount in the account after 5years will be $3172.5.
simple interest -
Simple interest is a quick and simple way to figure out how much money has earned interest.
Criag has amount in the bank, P = $2700
rate of interest, R = 3.5%
Time period, T = 5years
simple interest = (P X R X T )/100
SI = (2700 X 3.5 X 5)/ 100
SI = $472.5
Amount = principle + simple interest
Amount = 2700 + 472.5
Amount = $3172.5.
Craig has$2700 in the bank. The amount in the account after 5years will be $3172.5.
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in the figure below ABC ~ DEF and the area of ABC is equal to 30 square units. what is the area of DEF?
The formula for determining the area of a traingle is expressed as
Area = 1/2 * base * height
For triangle ABC,
height = 6
area = 30
Thus,
30 = 1/2 * base * 6
30 = 3 * base
base = 30/3 = 10
If two triangles are similar, it means that the ratio of their corresponding sides is equal. Thus,
Height of traingle ABC/ Height of traingle DEF = Base of traingle ABC/ base of traingle DEF
Thus, we have
6/Height of traingle DEF = 10/15
6/Height of traingle DEF = 2/3
By cross multiplying, we have
2 * Height of triangle DEF = 3 * 6 = 18
Height of triangle DEF = 18/2 = 9
Thus, area of triangle DEF is
Area = 1/2 * 15 * 9 = 67.5
The correct option is C
What is 94.7 rounded to the nearest whole number?
1. Method Half Round Up
94.7 = 95
2. Method Half Round Down:
94.7 = 95 (Only 94.5 will be rounded to 94)
6.68 rounded to the nearest tenth:
6.7 (only one decimal place)
Find the slope and they intercept of the line in the groch, % 5
We need to form the next equation of the line
[tex]y=mx+b[/tex]First, we need to calculate the slope, with the next formula
[tex]m=\frac{y2-y1}{x2-x1}[/tex]so we need two points, we can use either of the points in the line we have in the graph
For example, I will use
P1=(0,3)=(x1,y1)
P2=(-1,-2)=(x2,y2)
[tex]m=\frac{-2-3}{-1-0}=\frac{-5}{-1}=5[/tex]the slope m=5
the y-intercept (b) we can find it in two ways the first is observing the graph the y-intercept is where the line intercepts the y-axis
b=3
Also, we can calculate b with the formula at the begging and using one point
(y-3)=m(x-0)
we clear x
y=mx+3
then by the form, we can assume the value of b
b=3
Determine a series of transformations that would map Figure K onto Figure L.Press "try" to test a transformation or sequence oftransformations.y1211109Figure K7Figure-12-11-10-9-8-7-6-5-4-3-2-11 2 3 49 10 11 12-10- 11-12
To pass from figure K to figure L, the first step would be to reflect figure K over the y-axis.
To do so, you have to change the sign of the x-coordinate of every vertex of the figure, while leaving all y-coordinates unchanged, following the rule:
[tex]r_{y-\text{axis}}\colon(x,y)\to(-x,y)[/tex]At Cityville High School, 33% of the students participate in sports, 37% of the students participate in academic clubs, and 19% of the students participate in both sports and academic clubs. Find the proportion of students who participate in either sports or academic clubs.
Let's begin by listing out the information given to us:
Sports = 33% = 33/100 = 0.33
Academic clubs = 37% = 37/100 = 0.37
Sports and Academic clubs = 19% = 19/100 = 0.19
Remainder (Neither Sports nor Academic clubs) = 100 - (33 + 37 + 19)
= 100 - 99 = 1% = 1/100 = 0.01
We will find the proportion of students who participate in either sports or academic clubs by summing together the percentage of students that participate in Sports alone & those that participate in Academic clubs alone as shown below:
[tex]\begin{gathered} n=0.33+0.37=0.70 \\ n=0.7 \end{gathered}[/tex]Therefore, the proportion of students who participate in either sports or academic clubs is 70% or 0.7
16)Calculate the mean, mode, and midrange from the frequency table given below. Estimate the median.ValueFrequency129136144157164To find Mean: x = ∑ x nMode: The mode is the number that appears the most in given data which is ____ since it is given three times.Mode =To find Midrange:Mid−range = Max(x) + Min(x)2
In our table, we have the following set of values for the frequency:
[tex]\lbrace9,6,4,7,4\rbrace[/tex]The mean of a dataset is the sum of all elements divided by the total amount of elements. The mean of our set is:
[tex]\bar{x}=\frac{\sum_{i\mathop{=}1}^5x_i}{5}=\frac{9+6+4+7+4}{5}=\frac{30}{5}=6[/tex]The mean of the frequency is equal to 6.
The mode is the number that appears the most in given data which is 4 since it is given two times.
To find the median we need to reorder our dataset in ascending order.
[tex]\lbrace4,4,6,7,9\rbrace[/tex]The median is the middle number in a sorted, ascending or descending, list of numbers. In our problem, the middle element is 6, therefore, the median is 6.
The maximum value of our dataset is 9 and the minimum value is 4, therefore, the midrange is:
[tex]\frac{9+4}{2}=\frac{13}{2}=6.5[/tex]The midrange of the dataset is 6.5.
Select the correct answer from each drop-down menu.For all positive values of x, the value of1085Iis always
SOLUTION:
Case: Logarithm laws
Method:
The laws are:
[tex]\begin{gathered} \log_aa=1....(1) \\ \log_a1=0....(2) \end{gathered}[/tex]The logarithm of the same base is 1 while the logarithm of 1 is 0.
Final answer:
For all positive values of x, the value of
[tex]\log_xx\text{ }is\text{ }always\text{ }1[/tex]And the value of
[tex]\log_x1\text{ }is\text{ }always\text{ }0[/tex]A virus takes 16 days to grow from 100 to 190.How many days will it take to grow from 100to 760? Round to the nearest whole number.
The growth of the virus is considered exponential.
Thus the expression is,
[tex]N=N_oe^{kt}[/tex]Given,
A virus takes 16 days to grow from 100 to 190.
Thus,
[tex]190=100e^{16k}[/tex]Putting ln on both side we have
ln(190/100)=16k
0.64=16k
k=0.04
Similarly,
[tex]760=100e^{0.04t}[/tex]Solving,
ln(760/100)=0.04t
t=50.70
Thus required days is 51 (rounding off to whole number)
Express as a single, simplified logarithm. 1 − (510 + 253)
Answer:
[tex]=1-log\left(1432590\right)[/tex]Step-by-step explanation:
By the logarithm properties:
[tex]\begin{gathered} \log_(a*b)=\log_a+logb \\ \log_(\frac{a}{b})=\text{ log a - log b} \\ \log_(a^b)=b\log_a \end{gathered}[/tex]Therefore, for the given logarithm:
[tex]\begin{gathered} 1-(log510+log53^2) \\ =1-(log510+log2809) \\ =1-log\left(1432590\right) \end{gathered}[/tex]PRIOR KNOWLEDGE If f (x)=x^2-x I, what is f(-3)? A 12 b -6 c6 d12
to find f(-3) you just replace x=-3 on the equation
[tex]\begin{gathered} f(-3)=(-3)^2-(-3) \\ f(-3)=9+3 \\ f(-3)=12 \end{gathered}[/tex]so, the option is D
Determine if the situation below are biased or unbiased and explain why.The newspaper staff surveyed a group of students at a band concert about what their favorite elective is.
Explanation
We are given the following:
The newspaper staff surveyed a group of students at a band concert about what their favorite elective is.
We are required to determine if the situation is biased or unbiased and give the reason.
We know that in a biased sample, one or more parts of the population are favored over others, whereas in an unbiased sample, each member of the population has an equal chance of being selected.
Therefore, the situation is biased because the choice of students surveyed simply supports band over others.
A T-shirt company bought a new packaging and tacking systems for $100,000. The formula V = 100,000(1 – 0.125)models the value of the system, V, in dollars, after depreciation for y years. In this formula, what is the meaning of the term (1 -0.125)?
You have the folowing formula:
V = 100,000(1 - 0.125y)
for the value of the new system of the T-shirt company.
The factor (1 - 0.125y) means that each year the value of the system decrease in a factor of 0.125, which is equivalent to a decrese of 12.5%.
HENCE:
the value of the system will decrease by 12.5% each year
Help! I’ll mark u brainly and helps me now please
Start by typing the numbers: 4 (for the box that reads "Min" since the list of values (which they gave you already ordered from least to largets) is showing that the minimum value of your set is 4.
You can do the same with the number 16, placing it as the maximum "Max".
AT the same time, it seems that you can move the different parts of the box diagram, so please, grab the left end of the whisker of the box diagram, and move it to align with the number "4" in the horizontal axis.
Do also an adjustment of the right end of the whisker and take it to align with the number 16 in the horizontal axis.
The Median in this case (of even number of values in the set) is given by the average of the two numbers around the middle of the list. So you do : (6+9)/2 = 15/2 = 7.5
7.5 is the median.
The first quartile is for value 6, and the third quartile for the value 10.
So, please move the ends of the box to align with the numbers 6 and 10 on the horizontal axis, and the center of the box
the figures below are similar. the labeled sides are corresponding. what is the perimeter of the smaller square?
Pairs of similar figures have a constant ratio in all its length measures.
Perimeter is a type of length, and the measures of sides are too.
From the given sides, we can calculate this ratio:
[tex]r=\frac{3.9}{3.8}[/tex]Now, we can use this ratio to calculate the missing perimeter:
[tex]\begin{gathered} r=\frac{P_2}{P_1} \\ P_1=\frac{P_2}{r}=\frac{15.6}{(\frac{3.9}{3.8})}=15.6\cdot\frac{3.8}{3.9}=15.2 \end{gathered}[/tex]So, the perimeter is:
[tex]P_1=15.2in[/tex]Rachel drew a scale drawing of a city. The scale she used was 1 inch : 3 yards. The actual width of a neighborhood park is 51 yards. How wide is the park in the drawing?
In drawing the width of park is 17 inches.
what is scale factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure.
Scale factor is described as the number or the conversion factor which is used to adjust the size of a figure without changing its shape. It is used to expand or decrease the size of an object.
Given:
The scale chosen 1 inch= 3 yards.
Now, the actual width is 51 yards
So, in inch it would be
= 51/3
= 17 inches.
Hence, in drawing the width of park is 17 inches.
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Please help me with this!b = 0.26h - 18.85Solve for h
Given the equatiion:
b = 0.26h - 18.85
Let's solve for h.
To solve for h, take the following steps:
Step 1.
Rearrange the equation:
0.26h - 18.85 = b
Step 2.
Add 18.85 to both sides:
0.26h - 18.85 + 18.85 = b + 18.85
0.26h = b + 18.85
Step 3.
Divide all terms by 0.26
[tex]\begin{gathered} \frac{0.26h}{0.26}=\frac{b}{0.26}+\frac{18.85}{0.26} \\ \\ h=\frac{b}{0.26}+72.5 \end{gathered}[/tex]Let's simplify further:
[tex]\begin{gathered} h=\frac{1b}{0.26}+72.5 \\ \\ h=\frac{1}{0.26}b+72.5 \\ \\ h=3.846b+72.5 \end{gathered}[/tex]ANSWER:
h = 3.846b + 72.5
Find the polynomial function of lowest degree having zeros -2 and 5i
Answer
[tex]P(x)=(x^{3}+2x^{2}+25x+50)[/tex]Explanation
Given
• Polynomial function of lowest degree
,• Zeros -2 and 5i
Procedure
The zeros of the polynomial can be written as
[tex]\begin{gathered} x=-2 \\ x+2=0 \end{gathered}[/tex][tex]\begin{gathered} x=5i \\ x-5i=0 \end{gathered}[/tex][tex]\begin{gathered} x=-5i \\ x+5i=0 \end{gathered}[/tex]If we multiply each other we get:
[tex](x+2)(x-5i)(x+5i)=0[/tex]Multiplying the last two factors is the sum of two squares:
[tex](x+2)(x^2+25)=0[/tex]Finally, combining the terms and simplifying:
[tex](x\cdot x^2+2x^2+25x+50)=0[/tex][tex](x^3+2x^2+25x+50)=0[/tex][tex]P(x)=(x^3+2x^2+25x+50)[/tex]1. If a standard die is rolled twice find P (rolling odd both time)
To find the probability of rolling odd both time, we have to find the probabilty of an odd number, then we multiply that fraction twice. We know that the probability of an odd number is 1/2, since have of all numbers are odd, and the other half are even. So,
[tex]P=\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}[/tex]Therefore, the probability of rolling an odd number both time is 1/4.Use the following for questions 1 - 6.f(x) = 2x - 3g(x) = 6x2 - 7x - 3h(x) = x3 – 2x2 + 3x - 5==1. f(x) – g(x)2. g(x) + h(x)
To subtract g(x) from f(x), we simply have to plug in the given values of the function written above.
[tex]\begin{gathered} =f(x)-g(x) \\ =(2x-3)-(6x^2-7x-3) \end{gathered}[/tex]Then, solve.
First, eliminate the parenthesis by distributing the symbol/number outside of it to the numbers inside the parenthesis.
[tex]=2x-3-6x^2+7x+3[/tex]Next, combine similar terms. We have 2x + 7x and -3 + 3.
[tex]=9x-6x^2[/tex]Lastly, arrange the terms according to highest degree (highest exponent).
[tex]=-6x^2+9x[/tex]Hence, f(x) - g(x) = -6x² + 9x.