Given the following question:
Candle = 4 inches tall
Burns at a rate of 0.6 inches per hour
x = hours
[tex]4-0.6x=1.5[/tex]4 representing the height of the candle
0.6 representing the rate the candle burns
x = the amount of time in hours the candle burns
1.5 = the height of the candle after it burned for x hours
[tex]\begin{gathered} 4-0.6x=1.5 \\ 0.6x=4-1.5 \\ 0.6x=2.5 \\ x=2.5\div0.6 \\ x=4.166 \\ =4.166\text{ hours} \end{gathered}[/tex]The pollution of Linton is 12 times as great as a pollution of Ellmore. The combine population of both sounds is 9,646 people. What is the population of Linton?
Explanation
[tex]\begin{gathered} 12x+x=9646 \\ 13x=9646 \\ x=\frac{9646}{13} \\ x=742 \end{gathered}[/tex]The population of Linton is 742*12=8904
Answer
8904
Rewrite barrel as a unit rate. hour O A. barrel/hour B. 10 barrels/hour O C. To barrel/hour OD. 1 barrels/hour
Then the correct answer is A. 5/8 barrel/hour
7. Find the value of x in the figure below. Justify your answer. 4 pts 20° (x - 15)° X = Reason:
Answer
x = 85°
Explanation
The image of this question shows that the two angles 20° and (x - 15)° both sum up to give a right angle (90°). So,
20° + (x - 15)° = 90°
20° + x - 15° = 90°
x° + 20° - 15° = 90°
x + 5° = 90°
x = 90° - 5°
x = 85°
Hope this Helps!!!
Target is having a sale on bath towels usually bath towels cost $15 today I paid only $12 what percent of the original price did I pay for the bath towels
80%
1) Since the prices on Target dropped from $15 to $12 to find the equivalent percentage of $12 in comparison to $15 we need to write down the following ratio:
[tex]\begin{gathered} 15----100\% \\ 12----x\% \\ \frac{15}{12}=\frac{100}{x} \\ 15x=12\cdot100 \\ \frac{15x}{15}=\frac{1200}{15} \\ x=80\% \end{gathered}[/tex]Note that we cross multiplied that ratio and then on the second step we have divided both sides by 15.
2) Hence, I paid 80% of the original price that day
Can you pls help me with this question thank you
The expression we have is:
[tex]2x+5[/tex]In this expression, we have two terms: 2x and 5.
The elements in these terms are variables, coefficients, and constants.
A variable is a letter that can take different values, a coefficient is a number that accompanies the variable, and a constant is a number that does not have any variable next to it (its value will not change).
In this case:
2 is the coefficient,
x is the variable,
and 5 is the constant.
Answer: a) 5
Photo attached. Total cost as function of x = Domain of total cost function =
1. Identify the given from the statements.
• Let the side of the square base= s
• Height of the rectangular box be= h
,• Given that :
s^2h = 20ft^3
solving for sh: s^2h = 20
s^2=20/h
s*s/s = 20/h /s
s = 20/hs
• Therefore sh = 20/s
Expandingthe given statements , we learn that :
• Material cost for base per square foot = 20 cents
,• Material cost for sides per square foot = 18 cents
,• Material cost for the top per square foot = 14 cents
2. Calculate Total cost
Total cost = {(s^2*20) + 4(sh)*18 +s^2*14}cents
= 20s^2 + 72*20/s + 14s^2
=34s^2 + 1440/s
• Expressing Total cost in terms of x , let s = x .
• Then Total cost (x) = 34x^2 +1440/x
2. Calculating the domain of TC(x) =34x^2 +1440/x
x <0 or x> 0
Domain (-∞;0) U(0;∞)
Write an equation for a line perpendicular to y=-5x-3 and passing through the point (15,4)
1) We need to consider the fact that perpendicular lines described by linear functions have opposite and reciprocal slopes when compared to the original linear function.
2) So we can state that the perpendicular line to y=-5x-3 has a slope of :
[tex]m=\frac{1}{5}[/tex]3) Now, the next step is to plug into the Slope-intercept form the following point (15,4) and then find the y-intercept:
[tex]\begin{gathered} y=mx+b \\ 4=\frac{1}{5}(15)+b \\ 4=3+b \\ 4-3=b \\ b=1 \end{gathered}[/tex]4) Thus, the equation of a perpendicular line to the line described by the linear function y=-5x-3 is:
[tex]y=\frac{1}{5}x+1[/tex]
Arlene buys a phone case and charging cord for 15% off. The original cost of the phone case is $18. Her total discount is $4.20.Write and solve an equation to find the original price of the charging cord
The total discount in Arlene's purchase was 4.20, this includes the discount applied over both, the case and the charging cord. We already know the original price of the phone case, the discount applied and the value of the discount, use it to find the original price of the chargind cord:
[tex]\begin{gathered} 0.15(18+x)=4.20 \\ 18+x=\frac{4.20}{0.15} \\ 18+x=28 \\ x=28-18 \\ x=10 \end{gathered}[/tex]The original price of the charging cord is $10
Kinsley measured a city park and made a scale drawing the scale of the drawing was 13 millimeters and 5 meters if the actual width of the soccer field is 65 meters how wide is the field in millimeters
Kinsley measured a city park
Scale of drawing : 13 milimeter and 5 meter
Actual width is 65 meter
Let the field in Milimeter is x
So,
[tex]\begin{gathered} 13\text{ milimeters and 5 meters=x milimeters and 65 meters} \\ \frac{13}{5}=\frac{x}{65} \\ \text{Apply cross multiplication} \\ x=\frac{13\times65}{5} \\ x=\frac{13\times13}{1} \\ x=169 \\ Park\text{in milimeters = 169} \\ So, \\ 13\text{ milimeters and 5 meters=169 milimeters and 65 meters} \end{gathered}[/tex]Answer: 13 milimeters and 5 meters = 169 milimeters and 65 meters
Select all of the ordered pairs that are solutions to the equation y= -6x + 7
We must substitute each pair into our equation:
A. If we substitute point (1,1), we have
[tex]\begin{gathered} 1=-6(1)+7 \\ 1=-6+7 \\ 1=1 \end{gathered}[/tex]then, this point is a solution.
B. If we substitute point (-1,1), we have
[tex]\begin{gathered} 1=-6(-1)+7 \\ 1=6+7 \\ 1=13\text{ !!!} \end{gathered}[/tex]this means that this point is not a solution.
C. If we substitute point (-6,7), we have
[tex]\begin{gathered} 7=-6(-6)+7 \\ 7=36+7 \\ 7=43\text{ !!!} \end{gathered}[/tex]this means that this point is not a solution.
D. If we substitute point (3,-11), we have
[tex]\begin{gathered} -11=-6(3)+7 \\ -11=-18+7 \\ -11=-11 \end{gathered}[/tex]then, this point is a solution.
Therefore, the solutions are option A and D
RIn this figure, sin ZQOP = cos 2and cos ZROQ = sin 2
So, Sin QOP = QP/OQ = OPPOSITE/ Hyp
Then, cos PQO = QP/OQ = Adjacent/ Hyp
Using the same logic, Cos ROQ = RO/OQ = Adj/Hyp
Then, sin QPO = RO/OQ = Opp/Hyp
The expression(Toys =)equalsy"zsztwhere1, the exponent of y, is:s, the exponent of %, is:t, the exponent of X, is:Next Question
The given expression can be simplified as follows:
[tex]\frac{(x^4y^5z^5)^6}{(x^5y^5z)^5}=\frac{x^{24}y^{30}z^{30}}{x^{25}y^{25}z^5}=x^{-1}y^5z^{25}=\frac{y^5z^{25}}{x}[/tex]Compare with the given term as follows:
[tex]\frac{y^5z^{25}}{x}=\frac{y^rz^s}{x^t}[/tex]Therefore r, the exponent of y is 5
s, the exponent of z is 25
t, the exponent of x is 1.
What E is. if E=2 when W=15, find E when W=10
Since the elongation E varies directly with the weight W, they are related as follows
[tex]E=kW[/tex]where k is the constant of proportionality. In order to find k, we can substitute the given values, that is, when E=2, W=15, then we have
[tex]2=k\cdot15[/tex]Then, k is given as
[tex]k=\frac{2}{15}[/tex]Therefore, our formula for any E and W is
[tex]E=\frac{2}{15}W[/tex]Now, in order to find E in the second case, by replacing W=10, we get
[tex]E=\frac{2}{15}(10)[/tex]which yields
[tex]E=\frac{20}{15}=\frac{4}{3}[/tex]Therefore, the answer is
[tex]E=\frac{4}{3}[/tex]X-4-3-2-1012f(x)-6-4-1-2-5-8-16Which is a possible turning point for the continuousfunction f(x)?O(-3,-4)O (-2,-1)O (0,-5)O (1,-8)
Solution
[tex](-2,-1)[/tex]The final answer
Option B
I will show you a pic
Answer
The red line represents y = x + 1
The blue line represents y = 2x - 7
We can see that the two lines and equation intersect at (8, 9)
Solution
x = 8
y = 9
Explanation
The two equations are
y = x + 1
y = 2x - 7
To solve this graphically, we will plot the two equations on the same graph and the solution will exist at the point where the two lines meet.
To plot the lines for each of these equations, we will use intercepts to obtain two points on each line and then connect the two points to get each of the lines.
y = x + 1
when x = 0
y = x + 1
y = 0 + 1
y = 1
First point on the line is (0, 1)
when y = 0
y = x + 1
0 = x + 1
x = -1
Second point on the line is (-1, 0)
The two points are (0, 1) and (-1, 0)
y = 2x - 7
when x = 0
y = 2x - 7
y = 2(0) - 7
y = 0 - 7
y = -7
First point on the line is (0, -7)
when y = 0
y = 2x - 7
0 = 2x - 7
2x = - 7
Divide both sides by 2
(2x/2) = (-7/2)
x = -3.5
Second point on the line is (-3.5, 0)
The two points are (0, -7) and (-3.5, 0)
The graph of this question will now be presented under answer and the point of intersection will bw evident.
Hope this Helps!!!
✓ 2 ✓ 3 ✓4 Find the missing side length. Assume that all intersecting sides meet at right angles. Be sure to include the correct unit in your answer. 16 A 9 A 13 A Check PLUS EGEE E Com. Tune here to
the given diagram:
We have to find the value of DE
Since all the lines intersect at right angle
[tex]\begin{gathered} \text{Here, AC + DE = BF} \\ 5\text{ + DE =13} \\ DE=13-5 \\ DE=8\text{ ft} \end{gathered}[/tex]Answer : DE = 8ft
A biologist records the number and types of fish caught in a local lake during a 2-yearperiod. The biologist reports that 796 of the fish caught during this period were trout,whereas 43% of the fish caught were bass. These reports of the number of trout andbass at this lake are examples ofcumulative frequencies.percentile ranks.relative frequencies.smooth curves.
Record for the number and types of fish caught in a local lake during a 2-year
period
Fish caught during this period were trout = 796
Fish caught during this period were bass = 43%
Total percentile = 100%
Fish caught during this period were trout = 100 - percentage of fish caught during this period were bass
fish caught during this period were trout = 100 - 43 = 57%
Hence the reports of the number of trout and
bass at this lake are examples of percentile ranks
Hi, can you help me answer this question please, thank you!
We are asked to determine the test statistic for two populations. To do that we will use the following formula:
[tex]z=\frac{\bar{x_2}-\bar{x_1}}{\sqrt[]{\frac{SD^2_2}{n_2}+\frac{SD^2_1}{n_1}}}[/tex]Where:
[tex]\begin{gathered} \bar{x_1},\bar{x_2}=\text{ population means} \\ SD_1,SD_2=\text{ standard deviations} \\ n_1,n_2=\text{ population sizes} \end{gathered}[/tex]Substituting the values we get:
[tex]z=\frac{83.3_{}-75.4}{\sqrt[]{\frac{(17.8)^2_{}}{19}+\frac{(9.7)^2_{}}{12}}}[/tex]Solving the operations we get:
[tex]z=1.596[/tex]Therefore, the test statistic is 1.596.
To determine the P-value we will determine the probability that the test statistic is less than the value we determined. This is:
[tex]p-\text{value}=P(z<1.596)[/tex]The value of the probability we find it in the z-table using the value z = 1.596, we get:
[tex]p-\text{value}=0.9441[/tex]Therefore, the p-value is 0.9441.
At the end of the winter, coats are on sale for 75% off. Question: a. If a heavy coat was priced at $ 160, then how much money will you save since it is on sale?
$120
Explanation
remember
[tex]75\text{ \% =}\frac{75}{100}=0.75[/tex]it means you can find 75 % of any value, just by doing th product of the number and 0.75
[tex]\begin{gathered} 160\cdot0.75=120 \\ \end{gathered}[/tex]Hence, 75% is $120 ,
the discount is 120,the new price is 40
the money you save is the difference, it is 120
I hope this helps you
Find the better buy:14 oz of doritos for $2.50 or 22 oz of doritos for $3.99.Make sure you round everything up to the nearest cent
Answer:
Both
Explanation:
To determine the better buy, find the unit price for each of the purchase:
[tex]\begin{gathered} \text{14 oz of doritos }\cos ts\text{ \$}2.5 \\ \text{Unit Price=}\frac{\text{2.5}}{14} \\ =\$0.179\text{ per oz} \\ \approx\$0.18\text{ per oz} \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} \text{22 oz of doritos }\cos ts\text{ \$}3.99 \\ \text{Unit Price=}\frac{\text{3}.99}{22} \\ =\$0.181\text{ per oz} \\ \approx\$0.18\text{ per oz} \end{gathered}[/tex]Therefore, to the nearest cent, both are equal buys since they have the same value.
Volume of the box with the cone shape cut out of it. What are the side lengths of the box and what is the volume of the box/cube only?
Answer:
Side length of the box: 6 cm
Volume of the box/cube: 216 cm³
Volume of the box without cone: 190.88 cm³
Explanation:
The sides of a cube are all equal, so in this case, the side length of the box is 6 cm.
Then, the volume can be calculated as
Volume = side x side x side
Volume = 6 cm x 6 cm x 6 cm
Volume = 216 cm³
To know the volume of the box with the cone shape cut of it, we need to calculate the volume of the cone with the following equation
[tex]Volume=\frac{1}{3}\pi r^2h[/tex]Where π = 3.14, r is the radius and h is the height. The diameter of the cone is 4 cm, so the radius is
r = 4 cm/2 = 2 cm
Then, replacing r = 2 cm and h = 6 cm, we get
[tex]\begin{gathered} Volume=\frac{1}{3}(3.14)(2\text{ cm\rparen}^2(6\text{ cm\rparen} \\ Volume=\frac{1}{3}(3.14)(4\text{ cm}^2)(6\text{ cm\rparen} \\ Volume=25.12\text{ cm}^3 \end{gathered}[/tex]Now, the volume of the box without the cone shape is
V = 216 cm³ - 25.12 cm³
V = 190.88 cm³
So, the answers are
Side length of the box: 6 cm
Volume of the box/cube: 216 cm³
Volume of the box without cone: 190.88 cm³
1/4+3/8 in simplest term
3(t - 24) = 8t - 4(t + 15)
We need to solve the equation:
[tex]3(t-24)=8t-4(t+15)[/tex]Then:
[tex]\begin{gathered} 3(t-24)=8t-4(t+15) \\ 3t-72=8t-4t-60 \\ 3t-72=4t-60 \\ 3t-4t=-60+72 \\ -t=12 \\ t=-12 \end{gathered}[/tex]Therefore, t=-12.
List the values at which X has a local Minimum or no minimum. What is the local minima, if one exist?
Looking at the graph
we have that
The local minimum is at
x=-4 and x=1The values of the local minimum are
For x=-4 ------> y=-1
For x=1 -----> y=-1
The values of the local minimum are equal to -1Which values are solutions to the inequality below? Check all that apply. x^2
Answer:
11, 7, and -8
Tools - Question 4 The coordinate planle below shows the location of segment QR. 109Y 5 Q1-4,3) 70-9-8-7-6-5-4-3-3 2 3 4 5 6 7 8 9 TU R(8,-6) What is the unit distance between the two endpoints of the segment? Illuminate Education TM, Inc.
Apply the distance between 2 points formula:
[tex]D=\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]We have the points:
(x1,y1) = (-4,3)
(x2,y2) = (8,-6)
[tex]D=\sqrt[]{(8-(-4))^2+(-6-3)^2}=\sqrt[]{(8+4)^2+(-9)^2}=\sqrt[]{144+81}=\sqrt[]{225}=15[/tex]Distance = 15
Find the zeros of each function by using a graph and a table. f(x)=x^2+2x–24.
Explanation
Step 1
[tex]f(x)=x^2+2x-24[/tex]Zeros
A(-6,0) B(4,0)
because
[tex]\begin{gathered} f(x)=x^2+2x-24 \\ f(-6)=(-6)^2+2(-6)-24=36-12-24=0 \\ f(4)=4^2+2\cdot4-24=16+8-24=0 \end{gathered}[/tex]Step 2
table
[tex]\begin{gathered} (-6,0) \\ (4,0) \\ f(-1)=-1^2+2\cdot-1-24=1-2-24=-25 \\ (1,-25) \\ \end{gathered}[/tex]I hope this helps you
When Ruby works out, she spends 2 minutes stretching for every 15 minutes of exercise. If Ruby spends 15 minutes stretching, how long did she spend exercising?
The ratio of time spend for stretching to time spend for exercise remain same.
Equate the ratio of time spend for stretching to time spend for exercise in both cases.
[tex]\begin{gathered} \frac{2}{15}=\frac{15}{x} \\ x=\frac{15\cdot15}{2} \\ =112.5 \end{gathered}[/tex]So Ruby spend 112 and a half minute to spend 15 minutes in stretching.
So answer is 112.5 min or
[tex]112\frac{1}{2}[/tex]I have this question and I can’t figure it out
Hello!
First, let's remember about the integers numbers.
These numbers can be positive or negative (and include the number 0). The main characteristic is that these numbers don't have a decimal part.
Knowing it, we can say that are integers:
• -1,
,• 0,
,• 2,
,• -2.
In the number line, we'll have:
Use the Pythagorean theorem to find the length of this segment.
To find the length of the segment use the Pythagoras theorem below:
[tex]AC^2=AB^2+BC^2[/tex]From the graph, we have:
AB = 15 - 3 = 12
BC = 7 - 2 = 5
Let's solve for the length of the segment AC:
[tex]\begin{gathered} AC^2=12^2+5^2 \\ \\ AC^2=144+25 \\ \\ AC^2=169 \end{gathered}[/tex]Take the square-root of both sides:
[tex]\begin{gathered} \sqrt[]{AC^2}=\sqrt[]{169} \\ \\ AC\text{ = 13} \end{gathered}[/tex]Therefore, the length of this segment is 13
ANSWER:
13