Answer:
Step-by-step explanation:
The lowest common denominator of 38 and 56 is 24. This allows us to convert the two fractions into 924 and 2024 for the purpose of adding and subtracting them.
The LCM is 24
Reason: 6*8/2 = 48/2 = 24
We multiply the denominators 6 and 8, then divide by 2 which is the GCF of the denominators.
Then we can use this to add the fractions
5/6 + 3/8
(5/6)*(4/4) + (3/8)*(3/3)
20/24 + 9/24
(20+9)/24
29/24
Therefore, 5/6 + 3/8 = 29/24
A petrified stump that is 4 ft tall casts a shadow that is 2 ft long. Find the height of a tent that casts a 5 ft shadow
The petrified stump is 4 ft tall and cast a shadow that is 2 ft long .
2 ft shadow has a 4 ft height
5 ft shadow will have ? height
cross multiply
[tex]\begin{gathered} \text{height of tent = }\frac{5\times4}{2} \\ \text{height of tent = }\frac{20}{2} \\ \text{height of tent = 10 ft} \end{gathered}[/tex]29. How long will it take to double an investment at 3.7% compounded continuously? Round your answer to the nearest tenth of a year. years
The formula for compounding continuously is :
[tex]A=Pe^{rt}[/tex]where A is the future amount
P is the principal amount
e is a constant
r is the rate of interest
and
t is the time in years.
The question stated that the investment will be doubled, so the future amount will be twice the principal amount.
A = 2P
The rate of interest is 3.7%
e is a constant approximately equal to 2.71828..
Subsitute the values to the formula and solve the value of t :
[tex]\begin{gathered} A=Pe^{rt} \\ 2P=Pe^{0.037t} \\ 2=e^{0.037t} \end{gathered}[/tex]Take the natural logarithm of both sides,
note that ln e = 1
[tex]\begin{gathered} \ln 2=\ln e^{0.037t} \\ \ln 2=0.037t\ln e \\ \ln 2=0.037t(1) \\ t=\frac{\ln 2}{0.037}=18.73 \end{gathered}[/tex]The answer is 18.73 years
The volume of an iceberg that is below the water line is 2^5 cubic meters. the volume that is above the water line is 2^2 cubic meters. how many times greater is the volume below the water line than above it?
Let:
[tex]\begin{gathered} V_1\colon\text{ volume of iceberg below the water line} \\ V_2\colon\text{ volume of iceberg above the waterline} \end{gathered}[/tex]We want to finde some number k such that we can express the volume of the iceberg below the water line as the product of k and the volume of the iceberg above the waterline, this is:
[tex]V_1=k\cdot V_2[/tex]then, solving for k we have the following:
[tex]\begin{gathered} V_1=2^5m^3 \\ V_2=2^2m^3 \\ V_1=k\cdot V_2 \\ \Rightarrow k=\frac{V_1}{V_2}=\frac{2^5}{2^2}=2^{5-2}=2^3^{} \\ k=2^3 \end{gathered}[/tex]we have that k=2^3. This means that the volume of the iceberg above the water line is 2^3 times the volume of the iceberg below the water line
Use the sum and difference identities to rewrite the following expression as a trigonometric function of a single number.tan(80°) – tan (20)1 + tan(80°)tan (20
Okay, here we have this:
Considering the provided expression, we are going to use the tangent formula of a subtraction, and is the following:
[tex]\tan (A-B)=\frac{tan\mleft(A\mright)-tan\mleft(B\mright)}{1+tan\mleft(A\mright)tan\mleft(B\mright)}[/tex]We can see that the expression they provide us has the same form as that of the tangent of a subtraction, where A is equal to 80° and B is equal to 20°, so we obtain:
[tex]\begin{gathered} \frac{tan\left(80°\right)-tan\left(20°\right)}{1+tan\left(80°\right)tan\left(20°\right)} \\ =\tan (80\degree-20\degree) \\ =\tan (60\degree) \end{gathered}[/tex]Finally we obtain that the original expression is equal to tan(60°).
Convert from Point-Slope Form into Slope-Intercept Form. Show your work!1. y + 1 = 7(x + 2) 2. y – 1 = –2(x – 1) 3. y – 2 = 1/4(x – 1) 4. y – 4 = 3(x – 3)
1. y+10=7(x+2) (applying the distributive law to the right side of the equation)
y= 7x+14-10 (substracting 10 in both sides of the equality)
y=7x+4
2. y-1=-2(x-1) (applying the distributive law to the right side of the equation)
y-1=-2x+2 (adding 1 in both sides of the equality)
y=-2x+2+1 (simplifying)
y=-2x+3
3. y-2=1/4(x-1) (applying the distributive law to the right side of the equation)
y-2=x/4 -1/4 (adding 2 in both sides of the equality)
y=1/4(x) -1/4+2 (simplifying)
y=1/4(x) +7/4
4. y-4=3(x-3) (applying the distributive law to the right side of the equation)
y-4=3x-9 (adding 4 in both sides of the equality)
y=3x-9+4 (simplifying)
y=3x-5
l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l l
Evaluate ( (dx-4) dx 16 S (WX - 4) dx = ( (Type an exact answer in simplified form) 9
whats the rate of change in the equation 0.860(17) + 3.302.
Given:
Let y= 0.860(17) + 3.302
The rate of change is the same as the slope of the equation
Comparing the given equation with the standard for of the equation y =mx + b
Work each problem according to the instructions given.a. Solve:2r +3=8=Previewb. Find r when y = 0:2x + 3y = - 8T =Previewc. Find y when I = 0;21 + 3y =- 8y =Previewd. Solve for y:2x + 3y8y =Preview
a)
The given equationis expressed as
2x + 3 = - 8
To solve for x, the first step is to subtract 3 from both sides of the equation. We have
2x + 3 - 3 = - 8 - 3
2x = - 11
Finally, we would divide both sides of the equation by 2. We have
2x/2 = - 11/2
x = - 11/2
can you please help me
The slope intercept form is y = m x + b
We need to put the equation -x + 4y = -8 in this form
At first, add both sides by x
[tex]\begin{gathered} -x+x+4y=-8+x \\ 4y=-8+x \end{gathered}[/tex]Then divide both sides by 4 to make the coefficient of y = 1
[tex]\frac{4y}{4}=\frac{-8}{4}+\frac{x}{4}[/tex]-8/4 = -2
x/4 = 1/4 x
[tex]y=-2+\frac{1}{4}x[/tex]Now switch -2 and 1/4 x
[tex]y=\frac{1}{4}x-2[/tex]Let us find which choice is?
It is the first one for the equation
Let us choose the graph
For the graph, the line intersects the y-axis at (0, -2)
The slope is positive, then its direction to the right
The x-intercept is (8, 0)
Then it is the last graph you post with equation y = 1/4 x - 2
Do you see it
Points S and T are midpoints of the sides of triangle FGH.Triangle G H F is cut by line segment S T. Point S is the midpoint of side H G and point T is the midpoint of H F. The lengths of H T and T F are 6 centimeters. The lengths of H S and S G are 4 centimeters. The length of S T is 8 centimeters.What is GF?
The measure of length of GF is 16 cm.
Given that point S is the midpoint of side HG and point T is the midpoint of HF of triangle FGH, the line segment ST is parallel to the side GF, and the triangles FGH and TSH are similar with proportional sides, then:
[tex]\frac{GF}{ST}=\frac{FH}{TH}=\frac{GH}{SH}[/tex]
We are given the following;
FH = HT + FT = 6 + 6 = 12 cm [HT = FT = 6 cm]
GH = HS + GS = 4 + 4 = 8 cm [HS = GS = 4 cm]
ST = 8 cm
Substitute the given values, we will get the following;
[tex]\frac{GF}{8} =\frac {12}{6} = \frac{8}{4}\\\frac{GF}{8} =\frac {12}{6}\\\frac{GF}{8} = 2[/tex]
GF = 2 * 8 = 16 cm
Thus, the measure of the length of GF is 16 cm.
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How are these functions related? How are their graphs related
Notice that the difference between the two equations is the +5 on the right side of the second equation.
The graph of the following equations are as folllows:
For y=x:
For y=x+5:
Thus, the graph of y = x was shifted 5 units upward to obtain the graph of y=x+5.
Therefore, each value or output of y=x+5 is 5 more than the corresponding output of y=x. Consequently, the graph of y=x+5 is the graph of y=x translated up by 5 units.
Thus, the correct answer is option C.
i need help with math
Answer:
7
Step-by-step explanation:
opposite angles are the same
8z+18=74
8z=56
z=7
Answer:
7 is my final answer thank you
Step-by-step explanation:
set as brainliest
.27 = as a percentage
.27 = as a percentage
To find out the number as percentage , multiply by 100
so
0.27*100=27%
Select the correct anawer Which of the following represents a function?
A function relates input to output. Functions can be one to one or many to one. The x values represent the input while the y values represent the output. In the case of one to one, it means that the output has only one corresponding input. Many to one means that there are many input values for one output value. An input value cannot have more than 1 output value. If this happens, then it is not a function. Looking at the options given,
Option A is a function since no input value has more than one output value
Option B is not a function since the output values of 7 and 1 has the same input value of - 1
For option C, the values are (- 3, - 2)' (- 1, 1), (- 1, - 5), (1, 4). It is not a function since the output values of 1 and - 5 has the same input value of - 1
Option D is not a function since the output values of 7 and 1 has the same input value of - 1
The correct option is A
2 5/6 divided by 1 3/4
Find the quotient. If possible, rename the quotient as a mixed number or a whole number. Write your answer in simplest form, using only the blanks needed.
The quotient is 113/21.
What is a mixed number?It is formed by combining three parts a whole number, a numerator and a denominator. Here, the numerator and denominator are a part of the proper fraction that makes the mixed number. These are also known as mixed fractions. It contains both an integer or a whole number. A mixed fraction or number is therefore a product of a whole number and a proper fraction.
2 5/6 = (2·6 +5)/6 = 17/6
1 3/4 = (1·4 +3)/4 = 7/4
Here 17/6 is dived by 7/4,we get
(17/6) ÷ (7/4) = (17/6) × (4/7) = (17×4)/(6×7) = (17×2)/(3×7) = 34/21
Here 34/21 is converted into a mixed number.
34/21 = (21 +13)/21 = 1 13/21
Therefore, the quotient is 113/21
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Describe the shape of the graph of the cubic function by determining the end behavior and number of turning points. y=2x^3-x-1 What is the end behavior of the graph of the function?
Solution
What is the end behavior of the graph of the function?
[tex]y=2x^3-x-1[/tex]The end behaviors of the function describe the functions of x as it approaches +∝ and as x approaches -∝
Therefore the correct answer is
Option D
Final answer = Down and Up
Turning points = 2
A group of 30 students rented small canoes and large canoes at a river park.
• The group
rented twice as many small canoes as large canoes.
• There were 3 students in each small canoe.
• There were 4 students in each large canoe.
Let x represent the number of small canoes and let y represent the number of large canoes
Create a set of equations that can be used to determine the number of each type of canoe the group rented.
Answer:
Im taking the test ill give the answers in 5 minutes
Step-by-step explanation:
Identifies which property it belongs to1) 15^8/5^32) (8^2)^1
Given the calculation
[tex]\frac{15^8}{5^3}[/tex]Second calculation
[tex](8^2)^1[/tex]810 А 30° E Given: Circle C. What is the value of angle x? B 99° 69° 132 30°
In this problem you can reflect the small triangle and you will see that the angle D is equal to the angle x, and the angle E is equal to the angle B so we can sum tyhe internal angles of the big triangle to find x so:
[tex]x+81+30=180[/tex]And we solve for x so:
[tex]\begin{gathered} x=180-81-30 \\ x=69 \end{gathered}[/tex]the angles x is equal to 69º
A researcher randomly purchases several different kits of a popular building toy. The following table shows the number of pieces in each kit in the sample. Find the standard deviation of the data. Round your answer to the nearest hundredth, if necessary.
The Solution:
Given:
We are required to find the standard deviation of the given data.
Find the sample mean of the given data.
Find the standard deviation of the data.
Therefore, the correct answer is 68.07
48, -24, 12, -6,... 50th term
For the next series we will calculate its expression
[tex]a_n=(-1)^{n+1}3\cdot2^{^{5-n}}[/tex]For n = 1
an = 48
For n = 2
an = -24
For n = 50
an = 8.5265128e-14
The mean per capita income is 24,653 dollars per annum with the standard deviation of 778 dollars per annum. What is the probability that the sample mean would be less than $24,745 if a sample of 441 persons is randomly selected? Round your answer to four decimal places
Remember that
[tex]z=\frac{x-μ}{\frac{σ}{\sqrt{n}}}[/tex]where
μ=24,653
σ=778
n=441
X=24,745
substitute
[tex]\begin{gathered} z=\frac{24,745-24,653}{\frac{778}{\sqrt{441}}} \\ \\ z=2.4833 \end{gathered}[/tex]using the values of the z-score table
we have that
P(x>2.4833) = 0.0065086
therefore
The answer is 0.0065which of the following expressions could be used to determine?
We have the following:
They tell us that the capacity is 350, therefore that is the maximum value, it means that we must subtract the exchange rate from this value, that is, the number od tickets per hour that are sold, 23
thus
[tex]350-23h[/tex]The answer is the option B.
Determine if the following equations are parallel, perpendicular, or neither. 7(x – 1) = 3y + 21 and 3.5x + 1.5y = 4.5
Given the two equations
7(x - 1) = 3y + 21
3.5x + 1.5y = 4.5
To determine if the lines are visible or perpendicular
Step 1: Expand the equations and make y the subject of the formula
7(x - 1) = 3y + 21
=> 7x - 7 = 3y + 21
=> 3y = 7x - 7 - 21
=> 3y = 7x -28
Divide both sides by 3
y = 7/3x - 28/3 ------equation 1
3.5x + 1.5y = 4.5
1.5y = -3.5x + 4.5
Divide both sides by 1.5
y = -3.5/1.5 x + 4.5/1.5
y = -7/3x + 3--------equation 2
Step 2: compare the two equations to the equation of a line, y = mx + c
For equation 1
m = 7/3
For equation 2
m= -7/3
The slopes are not the same
Also, the product of the gradients did not give -1
It can be seen that the lines are neither perpendicular nor parallel
-What is the product of (a - 1) and (2a + 2)?A 2(a2 - 2)B 2(a2 - 1)C a2 + 4a - 2D2a2 - 4a - 2-
The product of the sum and difference binomials is
[tex](x-y)(x+y)=x^2-y^2[/tex]We will use this rule to solve the question
We need to find the product of (a - 1) and (2a + 2)
At first, we will take 2 as a common factor from the second bracket
[tex]\begin{gathered} 2a+2=2(\frac{2a}{2}+\frac{2}{2}) \\ 2a+2=2(a+1) \end{gathered}[/tex]Now, we will multiply (a - 1) by 2(a + 1)
[tex](a-1)(2a-2)=2(a-1)(a+1)[/tex]By using the rule of the product of the sum and difference above, then
[tex]\begin{gathered} 2(a-1)(a+1)=2(a^2-1^2) \\ 2(a-1)(a+1)=2(a^2-1) \end{gathered}[/tex]The answer is B
Watch help videoKevin has a bag that contains orange chews, strawberry chews, and peach chews. Heperforms an experiment. Kevin randomly removes a chew from the bag, records theresult, and returns the chew to the bag. Kevin performs the experiment 32 times. Theresults are shown below:An orange chew was selected 5 times.A strawberry chew was selected 17 times.A peach chew was selected 10 times.Based on these results, express the probability that the next chew Kevin removesfrom the bag will be peach chew as a percent to the nearest whole number.Answer:Submit Answer
Divide the amount of times that a peach chew was selected over the total number of times that the experiment was performed to find the probability that the next chew will also be a peach chew:
[tex]\frac{10}{32}=0.3125=31.25\text{ \%}[/tex]Then, as a percent to the nearest whole number, the probability that the next chew Kevin removes from the bag will be a peach chew, is:
[tex]31\text{ \%}[/tex]Cuanto es 123 x 200?
Answer:
[tex]123\times200=24600[/tex]Explanation:
We want to find the product of 123 and 200;
Therefore, the product of 123 and 200 is;
El producto de 123 y 200 es;
[tex]123\times200=24600[/tex]A school librarian would like to buy subscriptions to 7 new magazines. Her budget however, will allow her to buy only 4 new subscriptions. How many different groups of 4 magazines can she chose from the 7 magazines?
The number of groups of 4 magazines can she choose from the 7 magazines is 35
Total number of magazines that school librarian would like to buy subscription = 7 magazines
The number of subscription that she can afford = 4 new subscription
The different groups of 4 magazines can she choose from the 7 magazines = [tex]7C_4[/tex]
The combination is the method of selecting a particular items or objects from the group of collection. The combination can also be defined as the number of possible arrangement from the collection.
Then the value of
[tex]7C_4[/tex] = 7! / 4!(7 - 4)!
= 7! / (4! × 3!)
= (7 × 6 × 5 × 4!) / (4! × 3!)
= (7 × 6 × 5) / 3!
= (7 × 6 × 5) / 3 × 2 × 1
= 210 / 6
= 35
Hence, the number of groups of 4 magazines can she choose from the 7 magazines is 35
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Can someone please help me with this math, thank you
Given data:
The given growth rate is r=7.8%=0.078.
The final number of bacteias in terms of initial is P'=2P.
The expression for the bacterias growth rate is,
[tex]P^{\prime}=P(1+r)^t[/tex]Substitute the given values in the above expression.
[tex]\begin{gathered} 2P=P(1+0.078)^t \\ 2=(1.078)^t \\ \ln (2)=t\ln (1.078) \\ t=\frac{\ln(2)}{\ln(1.078)} \\ =9.23\text{ hours} \end{gathered}[/tex]Thus, after 9.23 hours population of the bacterias doubled.
what is the value of the expression when m=2 and n=-3. (4m^-3n^2)^2
Giving the funtion
[tex](4m^{-3}n^2)^2[/tex]m=2
n=-3
[tex](4(2)^{-3}(-3)^2)^2[/tex][tex](\frac{4}{2^3}(9))^2[/tex][tex](\frac{36}{2^3})^2[/tex][tex](\frac{36^2}{2^6})[/tex][tex](\frac{2^49^2}{2^2*2^4})=\frac{9^2}{2^2}[/tex][tex]\frac{81}{4}[/tex]then the evaluated function in m=2 n=-3
has a value of 81/4