Answer:
Yes
Step-by-step explanation:
5 x 3= 15
2 x 3= 6
Since they are multiplied by the same number to get to 15/6 they are equivalent fractions
3^10=3^7*x^3 solve for x
The value of x is 3.
What is the law of exponents?One of a set of rules in algebra: exponents of numbers are added when the numbers are multiplied, subtracted when the numbers are divided, and multiplied when raised by still another exponent: [tex]a^{m}.a^{n} = a^{m+n}[/tex], [tex]\frac{a^{m} }{a^{n} } = a^{m-n}[/tex]
Given that, [tex]3^{10} = 3^{7} x^{3}[/tex]
On solving, we get,
[tex]3^{10} = 3^{7} x^{3}[/tex]
[tex]\frac{3^{10} }{3^{7} } = x^{3}\\3^{10-7} = x^{3} \\3^{3} = x^{3} \\x = 3[/tex]
Hence, The value of x is 3.
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dry concrete can be made by mixing sand gravel and cement into the ratio 1:3:5 if you want 1800kg of dry cement , how much would you need
The amount of sand = 200 kg
The amount of gravel = 600 kg
The amount of cement = 1000 kg
What is mean by Ratio?
A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.
Where, x and y are individual amount of two quantities.
And, Total quantity gives after combine as x + y.
Given that;
Dry concrete can be made by mixing sand, gravel and cement into the ratio 1 : 3 : 5.
And, They want 1800 kg of dry concrete.
Now,
Since, Dry concrete can be made by mixing sand, gravel and cement into the ratio 1 : 3 : 5.
So, We can formulate;
The amount of sand = x
The amount of gravel = 3x
The amount of cement = 5x
Hence, We get;
⇒ x + 3x + 5x = 1800
Solve for x as;
⇒ x + 3x + 5x = 1800
⇒ 9x = 1800
⇒ x = 1800/9
⇒ x = 200
Thus, The amount of sand = x = 200 kg
The amount of gravel = 3x = 3 × 200 kg
= 600 kg
The amount of cement = 5x = 5 × 200 kg
= 1000 kg
Therefore, We get;
The amount of sand = 200 kg
The amount of gravel = 600 kg
The amount of cement = 1000 kg
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Onions are on sale at four different grocery stores. Which store offers thelowest unit rate for onions, in dollars per pound?$3.20• Farm Fresh:4 pounds• Mother Nature:1 pound$1.70• Hobson's:2 pounds• Veggie Delight: $0.70/poundO A. Farm FreshOB, Veggie DelightOC. Mother NatureD. Hobson's
T determine which store offers the lowest unit rate for onions ($/pound) you have to express calculate the price per pound for each grocery store and then compere the results.
To calculate the price per pound you can use corss multiplication
Farm Fresh
4pounds _____$3.20
1pound____$x
[tex]\begin{gathered} \frac{3.20}{4}=\frac{x}{1} \\ x=\frac{3.20}{4} \\ x=0.80 \end{gathered}[/tex]The onions cost $0.80 per pound
Mother nature
1/3pound ____$1/4
1pound____$x
[tex]\begin{gathered} \frac{\frac{1}{3}}{\frac{1}{4}}=\frac{x}{1} \\ x=\frac{1}{3}\cdot\frac{4}{1} \\ x=\frac{4}{3}\cong1.33 \end{gathered}[/tex]The onions cost $1.33 per pound
Hobson's
2pounds_____$1.70
1pound____$x
[tex]\begin{gathered} \frac{1.70}{2}=\frac{x}{1} \\ x=\frac{1.70}{2} \\ x=0.82 \end{gathered}[/tex]The onions cost $0.82 per pound
Veggie Delight
$0.70 per pound
Chang drove 871 miles in 13 hours. At the same rate how long would it take him to drive 536 miles?
Answer:
8 hours
Step-by-step explanation:
You need to find time per every mile.
So you do 13/871 which is 0.0149253731 miles for every hour.
You multiply that number by 536 which gets you 7.99999998 hours which allows you to round to 8 hours.
The table below gives the dimensions of a statue and a scale drawing of the statue.Find the scale factor of the drawing to the real statue.Write your answer as a fraction in simplest form.Height (inches)Length (inches)Scale factor:Drawing8006Statue6448 I need help with this math problem.
Given:
Find-:
The scale factor
Explanation-:
The scale factor is:
[tex]S.F.=\frac{\text{ Status}}{\text{ Drawing}}[/tex][tex]S.F.=\frac{64}{8}\text{ or }\frac{48}{6}[/tex]So, the scale factor is:
[tex]\begin{gathered} S.F.=\frac{64}{8}\text{ or }\frac{48}{6} \\ \\ S.F.=8\text{ or }8 \\ \\ S.F.=8 \end{gathered}[/tex]The scale factor is 8.
eah built a tower that was 1 m 34 cm tall. Then, she added on an antenna that was 98 cm. How tall is the tower now? 1 m = 100 cm
Answer:
232cm (2m 32cm)
Step-by-step explanation:
1m 34cm = 134cm
134cm + 98cm = 232 cm
Joe borrowed $9,000 from the bank at a rate of 7% simple interest pa year. How much interest did he pay in 5 years? In 5 years, Joe pays ? In Interest
Principal = 9000
Interest rate = 7% = 0.07
Time = 5 years
Simple interest formula:
A = P(1 + rt)
In this case:
A = 9000(1 + 0.07*5) = 9000(1 + 0.35) = 9000(1.35) = 12150
Interest = A - P = 12150 - 9000 = 3
calculate the average speed of a lion that runs 45 m in 5 seconds
Answer:
9 m /s
Step-by-step explanation:
To find the speed, take the distance and divide by the time
45 m/ 5 s
9 m /s
Answer:
[tex] \sf9ms ^{ - 1} [/tex]
Step-by-step explanation:
[tex] \sf \: Average \: speed = \frac{ Total \: distance }{Total \: Time}[/tex]
Let us find the average speed now.
[tex] \sf \: Average \: speed = \frac{ Total \: distance }{Total \: Time} \\ \sf \: Average \: speed = \frac{ 45m }{5s} \\ \sf \: Average \: speed = 9ms ^{ - 1} [/tex]
2.1 Simplify without using a calculator. 2.1.1 √√125 -√√
[tex] \sqrt{125 - \\ \sqrt{ \frac{1 \\ }{?} } } [/tex]
-
can someone help and explain how to do this. Ive been stuck in this lesson for days. This is so confusing and hard.
-3x plus 12y equivalent expressions
The equivalent expression for -3x + 12y is 3 (-x + 4y).
What are expressions?Expressions include a statement, at least one arithmetic operation, and at least two numbers or variables.
Given equation:
-3x + 12y
Take 3 as common from both the term, and we get,
= 3 (-x + 4y) so the equivalent expression will be 3(-x + 4y).
Therefore, the equivalent expression for -3x + 12y is 3 (-x + 4y).
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Select the correct difference.-325 - (-725)4 z4 25-10 25-45
Given:
-325 - (-725)
We know that negative negative equals positive
(- -) = +
Therefore, we have:
-325 - (-725)
= -325 - -725
= -325 + 725 = 400
ANSWER:
400
There is a population of 205 tigers in a national park. They are being illegally poached at the rate of 7tigers per year.Assume the population is otherwise unchanging, write a linear model using "P" for population and "t" fortime.What does the t-intercept signify?NOTE: This answer will NOT be automatically graded and will appear as a 0 until the instructor hasgraded it.Question Help: Message instructorSubmit Question
Solution.
Initial population = 205
After 1 year, population = 205 - 7 = 198
After 2 years , population = 198 - 7 = 191
After 3 years , population = 191 - 7 = 184
We can generate a table of value for the changes
[tex]\begin{gathered} Slope\text{ of the line, m = }\frac{198-205}{1-0} \\ m=-\frac{7}{1} \\ m=-7 \end{gathered}[/tex]One point on the line = (0, 205)
[tex]\begin{gathered} The\text{ equation of the linear model can be gotten using the formula} \\ y-y_1=m(x-x_1) \\ y-205=-7(x-0) \\ y-205=-7x \\ y=-7x+205 \\ Replacing\text{ y with P and x with t} \\ The\text{ linear model is P = -7t + 205} \end{gathered}[/tex]The t-intercept signifies the time when the population of the tiger will be zero. That is the time when there will be no more tigers in the park
Answer:
Step-by-step explanation:
bbbbbbbbbbb
The value of 41 squared is between which two whole numbers?
The image shows the square root of 41
The root of 41 in decimal is 6.403.
As such the integers before and after 6.403 are 6 and 7
Another way to solve this is to consider the perfect square before 41 which is 36.
The square root of 36 is 6. Since 41 is higher than 36, the number before root 41 would be 6 and the next number after 6 is 7.
Hence the two numbers before and after √41 are 6 and 7
i inserted a picture of the question, i can give you the answer to the previous question if it helps. C(t) = -0.30(t-12)^2 + 40
Answer:
F(t) = -0.54(t - 12)² + 104
Explanation:
We know that C(t) = -0.30(t - 12)² + 40 and F(t) = 9/5C(t) + 32
Then, we can replace C(t) on the equation of F(t) to get
[tex]\begin{gathered} F(t)=\frac{9}{5}C(t)+32 \\ F(t)=\frac{9}{5}(-0.30(t-12)^2+40)+32 \\ F(t)=\frac{9}{5}(-0.30)(t-12)^2+\frac{9}{5}(40)+32 \\ F(t)=-0.54(t-12)^2+72+32 \\ F(t)=-0.54(t-12)^2+104 \end{gathered}[/tex]Therefore, the new function F(t) is
F(t) = -0.54(t - 12)² + 104
what is a probability of surveying a student that is in math Spanish and chemistry round to the three decimal places
From the figure, the total number of students is
[tex]\begin{gathered} N=70+3+17+15+5+60+85+5 \\ N=260 \end{gathered}[/tex]The number 15 is common in spanish, chemistry and math.
Hence, the number of students studying spanish, chemistry and math, n=15.
Therefore, the probability of surveying a student that is in math Spanish and chemistry is,
[tex]\begin{gathered} P=\frac{n}{N} \\ P=\frac{15}{260} \\ P=0.058 \end{gathered}[/tex]Therefore, the
GG is considering two websites for downloading music. The costs are detailed here.
Website 1: a yearly fee of $15 and $5 for each download
Website 2: $7 for each download
Select the equation for Website 1.
Responses
y=15x+5
y=5x+15
y=−7x
y=7x
The equation for Website 1 is y = 15 + 5x option (A) is correct if yearly fee of $15 and $5 for each download
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
GG is considering two websites for downloading music.
Website 1: a yearly fee of $15 and $5 for each download
Let x be the number of downloads
Equation for the website 1:
Total cost is y
y = 15 + 5x
Thus, the equation for Website 1 is y = 15 + 5x option (A) is correct if yearly fee of $15 and $5 for each download
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Find the equation of the line that passes through the points (-3,-4) and (3,2)
The equation of the line which passes through points (-3,-4) and (3,2) is y = (2/3)x - 2.
What does the slope intercept form entail?A line's equation can be written in the slope-intercept form such that the slope as well as y-intercept are clearly visible. The line's slope is its its steepness, and the y-intercept is where the line intersects the y-axis.The data in the given question is-
The passing points are-
(x1, y1) =(-3,-4) and
(x2, y2) = (3,2)
Slope = m = (y2 - y1)/(x2 - x1)
m = (2 + 4)/(3 + 3)
m = 6/9
m = 2/3
Equation of the line is evaluated using slope intercept form.
y - y1 = m (x - x1)
y + 4 = (2/3)(x + 3)
y = (2/3)x - 2
Thus, the equation of the line which passes through points (-3,-4) and (3,2) is y = (2/3)x - 2.
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Can somebody help me with 2.) C? Thx, this is Algebra 2.
SOLUTION
Step 1 :
We need to list the transformation for the equation,
[tex]y\text{ = -}\frac{1}{5}x^2\text{ -3}[/tex]compared to the parabola parent function,
[tex]y=x^2[/tex]Step 2 :
We need to graph the function,
[tex]\begin{gathered} y\text{ = -}\frac{1}{5}x^2\text{ - 3} \\ \text{compared to the parabola parent function, y =x}^2 \end{gathered}[/tex]Step 3 :
The graph is as shown below:
Step 4 :
Based on the two graphs, we can see that:
The transformations are Reflection, Vertical Shift and Vertical Compression.
a tree standing vertically on level ground casts a 118 foot long shadow. the angle of elevation from the end of the shadow to the top of the tree is 22.3 degrees. find the height of the tree to the nearest tenth of foot.
Since the situation forms a right triangle, we can apply trigonometric functions:
Tan a = opposite side/ adjacent side
Where:
a= angle = 22.3°
opposite side = x
adjacent side = 118
Replacing:
Tan 22.3° = x / 118
Solve for x
Tan 22.3 * 118 = x
x = 48.4 ft
Please help quickly
The equation of the function in standard form is y = 3x -12.
How to write the equation of a function in a standard form when two points are given?
1. First find the slope using the slope formula, m = (y₂ - y₁) / (x₂ - x₁)
2. Find the y-intercept by substituting the slope and the coordinates of 1 point into the slope-intercept formula, y = mx + b.
3. Write the equation using the slope and y-intercept.
Here, we have
Points (2,-6) and (5, 3)
First we find the slope using the slope formula, m = (y₂ - y₁) / (x₂ - x₁), we get
m = (3 + 6) / (5 - 2)
m = 3
then, we find the y-intercept by substituting the slope and the coordinates of 1 point into the slope-intercept formula, y = mx + b.
we get,
-6 = 3*2 + b
-6 - 6 = b
b = 12
Now, we write the equation using the slope and y-intercept
we get,
y = mx + b
y = 3x - 12
Hence, the equation of the function in standard form is y = 3x -12.
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Pls, answer in a minute. PLS
Answer: The square will fit.
Step-by-step explanation:
the diameter of the circle is large enough that since the square is 7cm across, (each side is the same length, therefore the diameter is the same,) The square will fit on the inside of the circle.
(A) How many ways can a 2-person subcommittee be selected from a committee of 8 people?
To solve this problem, we have to use the combination formula
[tex]C^r_n=\frac{n!}{r!(n-r)!}[/tex]Where r represents the number of people for the subcommittee (2), and n represents the total committee (8). Replacing this information, we have
[tex]C^2_8=\frac{8!}{2!(8-2)!}=\frac{8!}{2!(6)!}[/tex]Remember that factorials are solved by multiplying the number in a reversal way, as follows
[tex]C^2_8=\frac{8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{(2\cdot1)(6\cdot5\cdot4\cdot3\cdot2\cdot1)}=\frac{40,320}{2(720)}=\frac{40,320}{1,440}=28[/tex]Therefore, there are 28 ways to form a 2-person subcommittee from a committee of 8.Logarithm 6) If log 5 = A and log 3 = B, find the following in terms of A and B:
Given the following parameters:
log 5 = A
log 3 = B
According to the law of product and quotient of logarithm as shown:
[tex]\begin{gathered} \log AB=\log A+\log B \\ \log (\frac{A}{B})=\log A-\log B \\ \log A^b=b\log A \end{gathered}[/tex]Applying the laws of logarithm in solving the given logarithm
[tex]\begin{gathered} a)\log 15 \\ =\log (5\times3) \\ =\log 5+\log 3 \\ =A+B \end{gathered}[/tex]For the expression log(25/3)
[tex]\begin{gathered} b)\log (\frac{25}{3}) \\ =\log (\frac{5^2}{3}) \\ =\log 5^2-\log 3 \\ =2\log 5-\log 3 \\ =2A-B \end{gathered}[/tex]For the expression log135
[tex]\begin{gathered} \log (135) \\ =\log (5\times27) \\ =\log (5^{}\times3^3) \\ =\log 5^{}+\log 3^3 \\ =\log 5+3\log 3 \\ =A+3B \end{gathered}[/tex]For the expression log₅27
[tex]\begin{gathered} \log _527 \\ =\frac{\log 27}{\log 5} \\ =\frac{\log 3^3}{\log 5} \\ =\frac{3\log 3}{\log 5} \\ =\frac{3B}{A} \end{gathered}[/tex]For the expression log₉625
[tex]\begin{gathered} \log _9625 \\ =\frac{\log 625}{\log 9} \\ =\frac{\log 5^4}{\log 3^2} \\ =\frac{4\log 5}{2\log 3} \\ =\frac{\cancel{4}^2A}{\cancel{2}B} \\ =\frac{2A}{B} \end{gathered}[/tex]For the value of 15, this can be expressed as shown. Since:
[tex]\begin{gathered} \log 5=A;10^A=5 \\ \log 3=B;10^B=3^{} \end{gathered}[/tex]Since 15 = 5 × 3, writing it in terms of A and B will be expressed as:
[tex]\begin{gathered} 15=5\times3 \\ 15=10^A\times10^B \\ 15=10^{A+B} \end{gathered}[/tex]Question 1 (1 point)
What integer represents a rise in temperature of 19°?
O a -|-191
Ob
-19
Oc
19
Od
-|19|
The integer which represents the rise in temperature of 19° is -|19|
Positive, negative, and zero numbers all fall under the category of integers. The word "integer" is a Latin word that signifies "whole" or "intact." Therefore, fractions and decimals are not considered to be integers.
A number without a decimal or fractional element is known as an integer, which encompasses both positive and negative numbers, including zero. The following are some examples of integers: -5, 0, 1, 5, 8, 97, and 3,043. Z denotes a collection of integers,
hence the correct form is answered.
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Triangle OPQ is similar to triangle RST. find the neasure of side ST. Round to the nearest tenth if necessary
By definition, when two figures are similar, their corresponding angles are congruent (this means that they have equal measure) and the ratios of the lengths of their corresponding sides are the same.
In this case you know that the triangles shown in the picture are similar, therefore, you can set up the following proportion:
[tex]\frac{OP}{RS}=\frac{PQ}{ST}[/tex]You can identify that:
[tex]\begin{gathered} OP=37 \\ RS=7 \\ PQ=48 \end{gathered}[/tex]Therefore, you can substitute values into the proportion:
[tex]\frac{37}{7}=\frac{48}{ST}[/tex]Now you have to solve for ST:
[tex]\begin{gathered} (ST)(\frac{37}{7})=48 \\ \\ ST=(48)(\frac{7}{37}) \\ \\ ST\approx9.1 \end{gathered}[/tex]The answer is:
[tex]ST\approx9.1[/tex]Find an equation of the line that satisfies the conditionPasses through (-1,-3) and (4,2)
The points given are:
(-1, -3) and (4, 2)
Coordinates are:
x₁ =-1 y₁=-3 x₂ = 4 y₂ = 2
First, let's find the slope(m) of the equation using the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]=\frac{2+3}{4+1}=\frac{5}{5}=1[/tex]Next, find the inetercept of the equation by substituting x =-1 y=-3 m = 1 into y=mx+ b
-3 = 1(-1) + b
-4 = -1 + b
Add 1 to bothside
-4+1 = b
-3 = b
b = -3
We can now form the equation of the line by simply substituting the value of m and b into y=mx+ b
y = x - 3
Therefore, the equation of the line that satisfies the condition is y = x - 3
I need guidance on finding the correct answers because I am confused
The Solution:
The correct answer is [option 4]
Given:
Required to select the correct statements.
[tex]\Delta ABC\cong\Delta DCB\text{ \lparen Reason: Side-Angle-Side Triangle Congruence Theorem}[/tex]Thus, the correct answer is [option 4]
two cards are drawn without replacement from a standard deck of 52 playing cards what is the probability of choosing a club and then without replacement a spade
occurringGiven a total of 52 playing cards, comprising of Club, Spade, Heart, and Spade.
[tex]\begin{gathered} n(\text{club) = 13} \\ n(\text{spade) =13} \\ n(\text{Heart) = 13} \\ n(Diamond)=\text{ 13} \\ \text{Total = 52} \end{gathered}[/tex]Probability of an event is given as
[tex]Pr=\frac{Number\text{ of }desirable\text{ outcome}}{Number\text{ of total outcome}}[/tex]Probability of choosing a club is evaluated as
[tex]\begin{gathered} Pr(\text{club) = }\frac{Number\text{ of club cards}}{Total\text{ number of playing cards}} \\ Pr(\text{club)}=\frac{13}{52}=\frac{1}{4} \\ \Rightarrow Pr(\text{club) = }\frac{1}{4} \end{gathered}[/tex]Probability of choosing a spade, without replacement
[tex]\begin{gathered} Pr(\text{spade without replacement})\text{ = }\frac{Number\text{ of spade cards}}{Total\text{ number of playing cards - 1}} \\ =\frac{13}{51} \\ \Rightarrow Pr(\text{spade without replacement})=\frac{13}{51} \end{gathered}[/tex]Thus, the probability of both events occuring (choosing a club, and then without replacement a spade) is given as
[tex]\begin{gathered} Pr(\text{club) }\times\text{ }Pr(\text{spade without replacement}) \\ =\frac{1}{4}\text{ }\times\text{ }\frac{13}{51} \\ =\frac{13}{204} \end{gathered}[/tex]Hence, the probability of choosing a club, and then without replacement a spade is
[tex]\frac{13}{204}[/tex]Given (x – 7)2 = 36, select the values of x.
Answer:
x = 1 , x = 13
Step-by-step explanation:
(x - 7)² = 36 ( take square root of both sides )
x - 7 = ± [tex]\sqrt{36}[/tex] = ± 6 ( add 7 to both sides )
x = 7 ± 6
then
x = 7 - 6 = 1
x = 7 + 6 = 13