a) addition;
+ | 9 | 7 | 2
6 | 15 | 3 | 6
3 | 6 | 15 | 6
12 | 5 | 6 | 17
b) multiplication;
x | 4 | 9 | 5
6 | 2 | 42 | 35
3 | 8 | 24 | 20
9 | 72 | 5 | 35
What is addition and multiplication?To find the missing values, look at each row and column individually and apply the appropriate addition rule.
In the first row, 9+7=16, so the missing value in the first row is 2.
In the second row, 6+15=21, so the missing value is 3. To find the other missing value, we can look at the first column. 3+9=12, so the missing value is 6.
In the third row, 3+6=9, so the missing value is 6. To find the other missing value, look at the second column. 6+15=21, so the missing value is 6.
In the last row, 12+5=17, so the missing value is 6. To find the other missing value, look at the third column. 6+6=12, so the missing value is 5.
For the appropriate multiplication rule:
In the first row, 5 is a factor, and the only possible value of x that can give 5 when multiplied by 5 is 1. Therefore, x=1, and fill in the rest of the row using multiplication: 1x4=4 and 1x9=9.
In the second row, 6 is a factor, and the only possible value of 42 that can be divided by 6 is 7. Therefore, 6x7=42. To find the missing value in the third column, divide 35 by 7, which gives 5.
In the third row, 4 is a factor, and the only possible value of 24 that can be divided by 4 is 6. Therefore, 4x6=24 for the third row. To find the missing value in the fourth column, divide 20 by 5, which gives 4.
In the last row, 9 is a factor, and the only possible value of 72 that can be divided by 9 is 8. Therefore, 9x8=72, for the last row. To find the missing value in the third column, we can divide 35 by 7, which gives 5.
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What is the term-to-term rule for this sequence? 64, 32, 16, 8, 4
Answer:
Divide by two is the term-to-term rule.
Step-by-step explanation:
64/2=32
32/2=16
16/2=8
8/2=4
Find the value of x for the following
The side has a length of 15 units.
Let us denote the length of the missing side by x. According to the Pythagorean theorem, the sum of the squares of the lengths of the two legs of a right triangle is equal to the square of the length of the hypotenuse. In mathematical terms, this can be written as:
side² + side² = hypotenuse²
Substituting the given values, we get:
x² + 8² = 17²
Simplifying this equation, we get:
x² + 64 = 289
Subtracting 64 from both sides, we get:
x² = 225
Taking the square root of both sides, we get:
x = 15
Therefore, the missing side has a length of 15 units.
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Katie's middle school graduation party will be at the skating rink. The cost for each person is $15. The cost of the room for the party's $80 katies parents have set a budget of $470.
26 kids can come on the budget of 470.
first subtract the 80 for the room then divided the rest by 15
Enter a number for y. Approximate to THREE decimal places (last digit should be 8). Thanks in advance!
Answer: 15.888
Step-by-step explanation:
You should use SOH CAH TOA or 30-60-90 rules. Since they are asking for approximate they probably want you to use SOH CAH TOA
They have given you the opposite of the angle and hypotenuse. The hypotenuse is always across from the right angle
You will use SOH
Sin 60 =y/18 mult both sides by 18
18 sin 60 =y
y=15.588
Irma has $41,000 in a savings account that earns 2% interest per year. The interest is not compounded.To the nearest cent, how much will she have in total in 4months?
Line xy is parallel to line segment ac as shown in the figure below.
Yes, students are correct. By AA similarity criterion, triangle XBY and triangle ABC are similar.
Given that, line XY is parallel to line segment AC.
Consider triangle XBY and triangle ABC,
∠X=∠A (Corresponding angles are equal)
∠Y=∠C (Corresponding angles are equal)
By AA similarity, triangle XBY and triangle ABC are similar.
Yes, students are correct. By AA similarity criterion, triangle XBY and triangle ABC are similar.
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Practice!
1.
In the diagram, JKLM~ EFGH.
C.
a.
b.
Find the scale factor of JKLM to EFGH.
k=
Find the values of x, y, and z.
x =
y =
Find the perimeter of each polygon.
4y + 4
H3G
11
zo
E 8 F
Z=
30
65°
M
20
D
K
L
Answer:
a. To find the scale factor of JKLM to EFGH, we can compare the corresponding sides:
JK/JH = KL/KG = LM/LF = x/x = 1
Therefore, the scale factor is 1.
b. Since JKLM~EFGH, the corresponding sides are proportional. We can set up the following ratios:
JK/EF = KL/FG = LM/FH = 1/1
JK/x = KL/20
LM/30 = 1/2
Solving for JK, KL, and LM:
JK = EF = x
KL = 20(1/2) = 10
LM = 30(1/2) = 15
c. To find the perimeter of JKLM, we add the lengths of its sides:
Perimeter of JKLM = JK + KL + LM + MJ
Perimeter of JKLM = x + 10 + 15 + x
Perimeter of JKLM = 2x + 25
To find the perimeter of EFGH, we can use the fact that corresponding sides are proportional:
FG = KL = 10
FH = LM = 15
EG = JK = x
EH = EF = x√2
Perimeter of EFGH = EF + FG + GH + EH
Perimeter of EFGH = x + 10 + 2z + x√2
We are not given a value for z, so we cannot calculate the perimeter of EFGH.
Note: The angle measures given in the diagram are not used in the calculations for this problem.
Polygon JKLM is drawn with vertices J(−2, −5), K(−4, 0), L(−1, 2), M (0, −1). Determine the image coordinates of M′ if the preimage is translated 4 units up.
M′(−4, −1)
M′(4, −1)
M′(0, −5)
M′(0, 3)
Answer: M′(−4, −1)
Step-by-step explanation: m=-2 j+-5+4=M′(−4, −1)
Answer:
Option D
Step-by-step explanation:
A company estimates that 0.8% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $200.
If they offer a 2 year extended warranty for $30, what is the company's expected value of each warranty sold?
Step-by-step explanation:
The expected value of each warranty sold can be calculated using the following formula:
Expected Value = (Probability of Failure without warranty x Replacement Cost without warranty) + (Probability of Failure with warranty x Replacement Cost with warranty) - Cost of Warranty
Probability of Failure without warranty = 0.8% or 0.008 (given)
Replacement Cost without warranty = $200 (given)
Probability of Failure with warranty = 0% (since the product is covered under warranty)
Replacement Cost with warranty = $0 (since the cost of replacement is covered under warranty)
Cost of Warranty = $30 (given)
Expected Value = (0.008 x $200) + (0 x $0) - $30
Expected Value = $1.60 - $30
Expected Value = -$28.40
The company's expected value of each warranty sold is -$28.40, which means that on average, the company can expect to lose $28.40 for every warranty sold. This is because the cost of the warranty ($30) is greater than the expected cost of replacement without the warranty ($1.60). Therefore, it is not beneficial for the company to offer the extended warranty.
The bar graph shows the number of Asturian households, in thousands, living in poverty from 1999 to 2004. The table holds a quadratic function for the data, where y is the number of households, in thousand living in poverty × years after 1999. 10. 10 1999 2000 2001 2002 2003 2004 QuadReg y = ax2 + bx + c a = 0.2299729818 b = - 0.4599459636 c = 7.5426446323 a. Use the table to express the model in function notation, with numbers rounded to two decimal places #(x) = 0.23x2 + - 0.46x + 7.54 b. According to the function in part (a), in which year was the number of households living in poverty at a minimum? 2000 (Round to the nearest year as needed.) c. Use the model to find the number of households, in thousands, for that year. 7400 (Round to one decimal place as needed.)
Answer:
a. The quadratic function for the data can be expressed in function notation as follows, rounding the coefficients to two decimal places:
#(x) = 0.23x^2 - 0.46x + 7.54
b. To find the year when the number of households living in poverty was at a minimum, we need to find the vertex of the parabola given by the quadratic function. The x-coordinate of the vertex is given by:
x = -b/(2a)
Substituting the values for a and b given in the problem, we get:
x = -(-0.4599459636)/(2*0.2299729818) ≈ 1
This means that the minimum occurs one year after 1999, i.e., in the year 2000.
c. To find the number of households living in poverty in the year 2000, we can substitute x = 1 in the function:
#(1) = 0.23(1)^2 - 0.46(1) + 7.54 ≈ 7.4
This means that there were about 7,400 households living in poverty in Asturias in the year 2000.
Step-by-step explanation:
The graph below
Which equation matches the graph?
Answer:
D
Step-by-step explanation:
A flower bed has the shape of a rectangle 5yards long 4 yards wide what is its area in square ft
The area of the flower bed is 180 square feet.
Area refers to the amount of space occupied by a two-dimensional shape or surface. It is measured in square units, such as square meters, square inches, or square centimeters. The area of a shape can be calculated by multiplying the length and width of the shape (in the case of a rectangle or square), or by using more complex formulas for other shapes, such as triangles or circles.
To convert yards to feet, we multiply by 3 since 1 yard = 3 feet.
The length of the rectangle in feet is 5 yards × 3 feet/yard = 15 feet.
The width of the rectangle in feet is 4 yards × 3 feet/yard = 12 feet.
The area of the rectangle in square feet is length × width = 15 feet × 12 feet = 180 square feet.
Therefore, the area is 180 square feet.
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What percent larger is 20.49 trillion to 13.4 trillion
The answer of the given question based on the percent is , 20.49 trillion is about 52.84% larger than 13.4 trillion.
What is Percentage?Percentage is a way of expressing a quantity or value as a fraction of 100. It is a widely used method for describing proportions, rates, changes, and comparisons in various fields such as mathematics, economics, statistics, science, and everyday life. The term "percent" literally means "per hundred", and it is represented by the symbol "%". To convert a number to a percentage, we multiply it by 100 and add the symbol "%".
To find the percent larger that 20.49 trillion is to 13.4 trillion, we can use the following formula:
Percent change = (New value -Old value) /Old value * 100%
Plugging in the values we have:
Percent change = (20.49 trillion - 13.4 trillion) / 13.4 trillion * 100%
= 7.09 trillion / 13.4 trillion * 100%
= 52.84%
Therefore, 20.49 trillion is about 52.84% larger than 13.4 trillion.
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Solve the following system of equations:
y=6−x
y=x2−6x+6
A. (1, 0), (-4, 1)
B. (0, 6), (5, 1)
C. (5, 8), (3, 6)
D. (-4, 12)
Answer:
B. (0, 6), (5, 1)
Step-by-step explanation:
y=6−x
y=x2−6x+6
6 - x = x² - 6x + 6
x² - 5x = 0
x(x - 5) = 0
x = 0 or x = 5
x = 0; y = 6 - 0; y = 6
x = 5; y = 6 - 5; y = 1
Answer: (0, 6), (5, 1)
The Venn diagram below shows the number of items in sets A and B.
An item is chosen at random.
a) Explain how we can tell from the Venn diagram that P(A) ≤ P(B) without doing any calculations.
b) Calculate P(A) and P(B) as fractions in their simplest forms.
B4
A1
9
A is inside B and 9 is outside the venn diagram
The probability of A would be lesser than or equal to that of B because A is a subset of B
Explaining P(A) ≤ P(B) from the Venn diagramFrom the question, we have the following parameters that can be used in our computation:
The Venn diagram
On the Venn diagram, we have
A is inside B
This means that A is a subset of B
And as such the probability of A would be lesser than or equal to that of B
Calculating P(A) and P(B)Here, we have
A = 1
B = 4
Outside = 9
So, we have
P(A) = 1/(1 + 4 + 9) = 1/14
P(B) = (1 + 4)/(1 + 4 + 9) = 5/14
Hence, the values of P(A) and P(B) are 1/4 and 5/14
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Statistics help!!!
I chose B and got it wrong, I still don’t understand how to get the correct answer or what that answer is, but I want to understand how to do it right !
What is the probability of rolling a single 6 sided dice three times and getting the following outcomes: 4, a number greater than two, and an
even number.
a) 4/9
b) 21/54 (wrong answer)
c) 1/27
d) 12/216
Answer:
I am not sure but I will say A I guess.
Find the volume of figure two
Answer: 72
Step-by-step explanation:
V=lwh
=(3)(4)(6)
=72
Find the reciprocal of the number. Check that the product of the number and its reciprocal is 1.
-7
The calculated value of the reciprocal of the number -7 is -1/7
Finding the reciprocal of a numberFrom the question, we have the following parameters that can be used in our computation:
Number = -7
As a general rule, the reciprocal of a number x is 1/x
Using the above as a guide, we have the following:
Reciprocal = -1/7 given that Number = -7
To check, we have
-1/7 * -7
Evaluate
Result = 1
Hence, the reciprocal is 1
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please answer this question
The measure of the angle m∠RTS in the circle is drives to be equal to 105°.
What are angles on same segment of a circleAny two angles that have the same endpoint that lie on the same segment of the circle, that is the region between the chord joining the endpoints of the angle and the arc not containing the angle are said to be equal in measure.
Thus;
m∠QPT = m∠RST
so; m∠RST = 34°
Considering the triangle RST, we can solve for m∠RTS as follows:
m∠RTS = 180° - (34 + 41)° {sum of interior angles of a triangle}
m∠RTS = 180° - 75°
m∠RTS = 105°
Therefore, the measure of the angle m∠RTS in the circle is drives to be equal to 105°
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Choose the equation for the graph.
a) y = 2x - 3| +1
b) y = -2|x - 3| +1
c) y = 2x - 3| - 1
d) y = -2|x + 3| -1
e) y = 2x + 3| +1
The calculated equation for the graph is y = -2|x + 3| - 1
Choosing the equation for the graph.From the question, we have the following parameters that can be used in our computation:
The absolute value graph
An absolute value function is represented as
y = a|x - h| + k
Where
Vertex, (h, k) = (-3, -1)
So, we have
y = a|x + 3| - 1
The graph faces down
So, a is negative
Possible value is a = -2
So, we have
y = -2|x + 3| - 1
Hence, the function is y = -2|x + 3| - 1
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A small manufacturing company makes $125 on each stereo sound bar produces, and $100 profit on each flatscreen TV it makes. Each sound bar and TV must be processed by cutting machine (A), a fitting machine (B), and a polishing machine(C). Each sound bar must be processed on machine A for one hour, machine B for one hour, and machine C for four hours. Each TV must be processed or machine A for two hours, Machine B for one hour, and machine C for one hour. Machine A is available for 16 hours machine B 49 machine C for 24 hours.
Giovanna deposited
5
$1600 into two different savings accounts.
She deposited half of the money at First Oak and the other half at West United.
How much interest will she have earned from both accounts at the end of 5 years?
(Round to the nearest cent)
Answer:
Since Giovanna deposited half of the money into each account, she deposited $1600 / 2 = $800 into each account.
Let's assume that First Oak offers an annual interest rate of r1, and West United offers an annual interest rate of r2. The amount of interest earned on each account after 5 years would be:
Interest earned on First Oak = $800 * r1 * 5
Interest earned on West United = $800 * r2 * 5
The total interest earned from both accounts would be the sum of these two amounts:
Total interest earned = $800 * r1 * 5 + $800 * r2 * 5
Total interest earned = $4000 * (r1 + r2)
We are not given the interest rates, so we cannot calculate the exact amount of interest earned. However, we can use the given information to make some observations.
Since we are looking for the total interest earned from both accounts, we can simplify the problem by assuming that the interest rates for both accounts are the same. In this case, we have:
Total interest earned = $4000 * 5 * r
Total interest earned = $20000 * r
To find the interest earned, we need to know the value of r. If, for example, the annual interest rate is 4%, then:
r = 0.04
Total interest earned = $20000 * 0.04
Total interest earned = $800
Therefore, if the interest rates for both accounts are the same and equal to 4%, Giovanna would have earned $800 in interest from both accounts at the end of 5 years. However, if the interest rates are different, the total interest earned would be different as well.
Without knowing the interest rates for the two accounts Giovanna deposited her money in, it's not possible to calculate the total interest she'd earn in 5 years. Normally, you would need to use the Simple Interest formula for each account and then add the two results together.
Explanation:This is a Mathematics question about simple interest, which can be solved using the formula: Interest = Principal × Rate × Time. Given that Giovanna divided her money equally into two accounts at First Oak and West United, she put $800 into each account. However, without information about the annual interest rates for both accounts, we can't calculate the amount of interest Giovanna would earn after 5 years. Once the specific interest rates for the two accounts are provided, one could use the Simple Interest formula for each account and then add the interest from both to get the total.
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hello, pls help
The distance AB is divided in the specified ratio. Calculate the coordinates of the division point T. A=(3|2|-1), B=(-6|1|-2), 1:2 Please help me because i am not sure if i did it right: T=A+r*(B-A) T=(3,2,-1)+1/3*(-9,-1,-1) T=(0,5/3,-4/3) Is it right? Pls help me
Yes, your answer is correct.
The coordinates of the division point T are indeed (0, 5/3, -4/3).
We have,
To find the coordinates of the division point T, we use the formula:
T = A + r(B - A)
where r is the ratio in which AB is divided.
In this case, the ratio is 1:2, so r = 1/3 (since 1 + 2 = 3).
Substituting the given values.
T = (3, 2, -1) + (1/3)(-9, -1, -1)
T = (3, 2, -1) + (-3, -1/3, -1/3)
T = (0, 5/3, -4/3)
Thus,
The coordinates of the division point T are indeed (0, 5/3, -4/3).
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Find the coordinate of point m
that partitions the segment Ab
In the ratio 3:4 if A 7,-3 and b -7,4
The coordinates of point M divides the line segment AB int he ratio 3 : 4 is given by ( 1, 0).
Ratio in which line segment AB divides m : n = 3 : 4
Let us consider the coordinates of A be ( x₁ , y₁ ) = ( 7, -3 )
Let us consider the coordinates of B be ( x₂ , y₂ ) = ( - 7 , 4)
Let us consider the coordinates of M be ( x , y )
Using the formula of line segment divides in the ration m: n we have,
x = ( mx₂ + nx₁ ) / ( m + n )
y = ( my₂ + ny₁ ) / ( m + n )
Substitute the values we have,
x = ( 3 × (-7) + 4 × 7 ) / ( 3 + 4 )
= ( -21 + 28 ) / 7
= 1
y = ( 3 × (4) + 4 × -3 ) / ( 3 + 4 )
= ( 12 - 12 ) / 7
= 0
Therefore, the coordinates of point M which partition the line segment AB is equal to ( 1, 0).
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The above question is incomplete, the complete question is:
Find the coordinate of point M that partitions the segment AB in the ratio 3:4,if A (7,-3) and B (-7,4).
There were 8 cows and 12 horses at a farm. 5 horses ran away. How many horses were left?
Answer:
Step-by-step explanation:
7 horses were left
Prove that ABC AADC.
51
51
2
B
Statement
D
1 m/BAC = m_DAC = 51
AB = AD=4
Pick statement
AABCEAADe
Reason
Pick statement
Given
Segments are the same length as themselves,
Pick congruence criterion
a hint
congruence
ΔABC and ΔADC are congruent by SAS
We have,
From the figure,
We have,
ΔABC and ΔADC
∠BAC = ∠DAC = 51 ( given )
AB = AD = 4 ( given )
AC = AC ( common length )
This means,
ΔABC and ΔADC are congruent by SAS
Thus,
ΔABC and ΔADC are congruent by SAS
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I need help with this problem if do thank you a lot
The area of the sector is 229.92 square inches and the length of the arc is 32.99 inches.
How to find area of the sector?
Follow is the formula of area of the sector,
Area of sector = [tex] \frac{θ}{360} \times πr²[/tex]
where θ is the angle of the sector in degrees, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14159.
Substituting the given values,
Area of sector
[tex]= \frac{135}{360} \times π \times 14² \\ = 0.375 \times π \times 196 \\ = 73.0875π[/tex]
≈ 229.92 square inches (rounded to two decimal places)
How To find the length of the arc?
The formula for the arc is [tex]Length \: of \: arc = \frac{θ}{360} \times 2πr[/tex]
Substituting the given values,
Length of arc = (135/360) × 2π × 14
= 0.375 × 2π × 14
= 32.9856
≈ 32.99 inches (rounded to two decimal places)
Therefore, the area of the sector is approximately 229.92 square inches and the length of the arc is approximately 32.99 inches.
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Question
Construct the exponential function that contains the points (0, 3) and (2, 75).
Provide your answer below:
f(x) = 0
The exponential function described is f(x) = 3*(5)^x
How to find the exponential function?A general exponential function can be written as:
f(x)= A*(b)^x
Where A is the initial value and b is the base.
Here we know that the function contains the point (0, 3), then:
f(0) = 3 = A*(b)^0
3 = A
We also know that the function contains (2, 75), then:
f(2) = 75 = 3*(b)^2
75/3 = b^2
25 = b^2
√25 = b = 5
The exponential function is.
f(x) = 3*(5)^x
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Name the similar triangles. ΔBAC ~ ΔDEF , ΔBAC ~ ΔEDF, ΔBAC ~ ΔDFE, ΔBAC ~ ΔFED
Based on the angle-angle similarity theorem (AA), the similar triangles in the image given can be named as: ΔBAC ~ ΔEDF.
What are Similar Triangles?When two triangles have the same shape but have different sizes, it means the triangles have corresponding pairs of congruent angles and corresponding pairs of sides that are proportional to each other. The triangles are said to be similar.
The image given show two set of triangles that have two corresponding pairs of congruent angles, based on the angle-angle similarity theorem, it means that they are similar to each other.
Therefore, the similar triangles are:
ΔBAC ~ ΔEDF.
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23. As long as supplies last, the local animal shelter will give customers a free collar and name tag for each dog or cat
adopted this month. The shelter has the following collars: 5 blue, 8 green, 2 purple, and 5 brown. The name tags that
are available are 10 plastic, 4 leather, and 6 metal.
What is the probability that the first customer will randomly be given a brown collar?
The probability that the first customer will randomly be given a brown collar is given as follows:
0.25 = 25%.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
The total number of collars is given as follows:
5 + 8 + 2 + 5 = 20 collars.
5 of these collars are brown, hence the probability that the first customer will randomly be given a brown collar is given as follows:
p = 5/20 = 1/4 = 0.25 = 25%.
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