If 30% of a number is 42 and 70% of the same number is 98, find 40% of that number.

If the functions be f(x) = 4x + 13 and g(x) = 10x − 2 then the expression (f + g)(x) be 4x + 11.

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.

Given f(x) = 4x + 13 and g(x) = 10x − 2

We must add both functions to reflect the amount of time it takes to travel east and west in order to calculate the round-trip time.

Let the equation be (f + g)(x) = f(x) + g(x)

substitute the values in the above equation, we get

= (4x + 13) + (10x − 2)

simplifying the above equation, we get

= 4x + 13 + 10x − 2

= 4x + 10x − 2 + 13

= 4x + 11

Therefore, the expression (f + g)(x) be 4x + 11.

The completed question is:

The function f(x) represents the time it takes an airplane to travel east. The function g(x) represents the time it takes an airplane to travel west. Given f(x) = 4x + 13 and g(x) = 10x − 2, solve for (f + g)(x) to determine the total roundtrip time.

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A 5-card poker hand is dealt from a standard deck of cards and the number of distinct ways are there to form a hand with two pairs are 1326 ways.

To solve this problem, we got to use permutations and the combinations. Given that a 5-card poker hand is dealt from a standard deck of cards  and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.

Here 4 suits with 13 different kinds for each and every suit , so number of total outcomes are 13*4 = 52

Here we use combinations, and given that a 5-card poker hand is dealt from a standard deck of cards  and with 4 suits and there are 13 different kinds for each and every suit and 13 different kinds are 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a.

The number of distinct ways are there to form a hand with two pairs are given by, C(52,2)

(52 * 51) / 2

(26 * 51)

1326 ways

Therefore, the  number of distinct ways are there to form a hand with two pairs are 1326 ways.

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Answer:

Step-by-step explanation:

Find common denominator.

1/x + x-1/9x = 1  => 9/9x + x-1/9x = 1  (The common denominator is 9x.)

Combine like terms.

9 + x - 1 / 9x = 1  =>  x + 8/ 9x = 1

Cancel out 9x from denominator. What you do to one side, you do to the other.

(9x)(x + 8/9x) = 1(9x)  =>  x + 8 = 9x

Solve for x.

8 = 8x  =>  x = 1  (subtract x from both sides at the beginning and then simplify.)

The amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.

A % in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

Formula for percentages: (Value/Total value) * 100

Dr. Grumman earned $141,340 in 2020.

The social security he paid is:

(141340)(6.2/100) = 8763.08

Hence, the amount paid to social security when Dr. Grumman earned $141,340 in 2020 is $8763.08.

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Answer:

B

Step-by-step explanation:

the zeros are the values of x on the x- axis where the graph crosses.

the graph crosses the x- axis at x = 3 and x = 6

then

the zeros are x = 3 and x = 6

Answer:

Step-by-step explanation:

We can start by finding the amount of water the leaky faucet loses in one hour:

5 gallons / 20 hours = 0.25 gallons per hour

This means that the leaky faucet loses 0.25 gallons of water every hour.

To find how many gallons of water the faucet will leak in 48 hours, we can multiply the rate of leakage per hour by the number of hours:

0.25 gallons/hour x 48 hours = 12 gallons

Therefore, the leaky faucet will lose 12 gallons of water in 48 hours.

Answer:

34

Step-by-step explanation:

The absolute value of a real number [tex]a[/tex] is [tex]a[/tex] when [tex]a[/tex] ≥ 0, or −[tex]a[/tex] when [tex]a[/tex] < 0. The absolute value of −34 is 34.

Hope it helps and have a great day! =D

The formula used to calculate the surface area of a square pyramid is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]

The square pyramid is the geometric shape that has a square base and 4 lateral face. The total number of faces will be five. The base shape is square and the side shape will be triangle. Number of edges in the square pyramid is eight

The surface area is the amount space covered by the surface of the object

Here the surface area of the square pyramid is

A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]

Where A is the surface area of the square pyramid

a is the base edge

h is the height of the square pyramid

Therefore, the surface area is A = a^2 + 2a[tex]\sqrt{\frac{a^2}{4}+h^2 }[/tex]

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We can make advantage of the distributive property of multiplication over addition, which says that a(b + c) = ab + ac. As a result, -55 is the simplified expression.

When you multiply a value by a sum, the distributive property of multiplication over addition is put to use. For instance, you wish to multiply 5 by the product of 10 plus 3. Since the numbers are similar terms, we typically add the numbers first and then multiply by 5=> 5(10 + 3) = 65.

An algebraic principle known as the distributive property indicates that it is necessary to multiply each of the two integers by the factor being multiplied by the sum or difference of two terms.

Using this property, we can expand the expression as follows:

(2 − 3)(7 2 − + 8) = 2(7 2 − + 8) − 3(7 2 − + 8)

Now we can simplify each term separately:

2(7 2 − + 8) = 2(49 − 2 + 8) = 2(55) = 110

and

−3(7 2 − + 8) = −3(49 − 2 + 8) = −3(55) = −165

Therefore, putting the results together, we have:

(2 − 3)(7 2 − + 8) = 110 − 165 = -55

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Among the continuous improvement tools listed in the query, the cause-and-effect (fishbone) diagram is often used to initiate a root cause analysis effort. This tool helps identify potential causes of a problem by breaking down a complex issue into smaller and more manageable components.

The diagram is shaped like a fishbone, with the problem at the head and the potential causes in the "bones" of the fish. By examining the various factors that could contribute to a problem, a team can begin to isolate the most likely root causes and develop targeted solutions to address them. Other tools like scatter plot, Pareto chart, and swim lane process map can also be useful in continuous improvement efforts, but they may not be the best choice for initiating a root cause analysis

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Answer: 5

Step-by-step explanation:

Answer: 10 times

Step-by-step explanation:

If he want to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually, then the multiplicative rate will be 0.98

The initial investment = $10000

decreasing percentage = 2%

Therefore, the second term will be the 98% of the first term

The first term = 10000

The second term = 10000 × 98/100

= 10000 × 0.98

= 9800

The common ratio is the ratio of the second term to the first term

The common ratio = second term / first term

= 9800 / 10000

= 0.98

Therefore, the multiplicative rate of change should Hal use in his function is 0.98

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The size of width of each lumber piece will be 3.875 inches.

Logic is the arrangement of all those concepts, whereas algebra is the study of abstract concepts.

Making something a little less complicated while both making it easier to attain or understand is the concept of clarity.

Mrs. Harris intends to divide the breadth of a piece of timber that is 11 ⁵/₈ inches broad into three equal pieces.

Convert the mixed fraction number to a decimal number. Then we have

11 ⁵/₈ = 11 + ⁵/₈

11 ⁵/₈ = 11.625 inches

The width of each lumber piece is given as,

⇒ 11.625 / 3

⇒ 3.875 inches

The size of width of each lumber piece will be 3.875 inches.

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Answer:

it's d. answer d. 57/76 is the probability of landing on black. that is roughly 3 times as much as the probability of landing in white 19/76. 19 X 3 = 60 which is roughly around the ballpark of 57.

The piecewise function's domain and range are all real numbers, excluding x = 6, and all real numbers, respectively.

The broad range of values within which we are permitted to enter into our function is known as the area of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it may take as input. After we enter an x value, the function outputs this sequence of values.

The piecewise function is a function.

In the image that is attached, a function is shown.

The function's defined values are its domain, and its attainable values are its range.

With the exception of the x = 6 range, all real numbers fall inside the domain.

As a result, choice c is the right one.

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Answer:  TRUE  Flóki reportedly released three ravens, and then sailed in the general direction that they flew, eventually discovering Iceland.

Step-by-step explanation:

(a) The angle measurement of first unknown angle is c = 80 degrees

(b) The angle measurement of second unknown angle is y = 110 degrees

Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.

(a) You can pick pair of starting angles a = 30 degrees and b = 70 degrees

The angle measurement of first unknown angle will be:

a + b + c = 180  (sum of angles in a triangle is 180 degrees)

c = 180 - a - b

c = 180 - 30 - 70

c = 80 degrees

(b) The angle measurement of second unknown angle will be:

y = 180 - b  (sum of angles on a straight line is 180 degrees)

y = 180 - 70

y = 110 degrees

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Ratio of the base of two triangles is 16:9 , if ratio of heights of two triangles is 3:4 and area 4:3.

It is given that the ratio of heights of two triangles is 3:4 and the ratio of area of two triangles is 4:3

We have to find the ratio of their base

The basic formula for the area of a triangle is equal to half the product of its base and height or  [tex]\frac{1}{2} \times base \times height[/tex]

Let b₁ , b₂ are the base of two triangles respectively

So, ratio of areas of triangles : [tex]\frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]

[tex]\frac{4}{3} = \frac{\frac{1}{2}\times b_{1} \times3}{\frac{1}{2}\times b_{2} \times4}[/tex]

[tex]\frac{b{1}}{b_{2}} =\frac{16}{9}[/tex]

So, ratio of the base of two triangles is 16:9

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The order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].

Using the given information, we can find the common ratio of the geometric sequence A.

First, we can use the equation T₂² = T₁ T4 to find T4. Substituting n = 4, we get:

T₂² = T₁ T4

20² = T₁ T4

T4 = 400/T₁

Next, we can use the equation T5 = 20 to find T₁r⁴:

T5 = T₁r⁴

20 = T₁r⁴

We can now substitute T4 in terms of T₁ in the equation above:

20 = T₁r⁴

20 = T₁(400/T₁)r⁴

20 = 400r⁴

r⁴ = 1/20

Therefore, the common ratio r = (1/20)^(1/4) = 0.5.

To find the order of the first term whose value is greater than 106, we can use the formula for the nth term of a geometric sequence:

Tn = T₁r^(n-1)

We want to find the smallest value of n such that Tn > 106. Substituting r = 0.5 and rearranging, we get:

T₁(0.5)^(n-1) > 106

T₁ > 212(0.5)^(1-n)

Since T₁ > 0, we can take the logarithm base 0.5 of both sides:

log(0.5)(T₁) < log(0.5)(212) + (n-1)

Solving for n, we get:

n > 1 + [log(0.5)(T₁) - log(0.5)(212)]

Therefore, the order of the first term whose value is greater than 106 is the smallest integer greater than 1 + [log(0.5)(T₁) - log(0.5)(212)].

Note that the exact value of this order depends on the value of T₁, which was not given in the original problem statement.

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Yes!

[tex](2^{2} )^{3}[/tex] = 2^6 = 64

(8-4)^2 = 4^2 = 16

then for the last part

4^-4 is the same as [tex]1/4^{4}[/tex] or 1/256

Then it is order of operations:

do 16 x 1/256 first which is 1/16

and then 64 - 1/16 to get 63 15/16 :)

PLEASE GIVE BRAINLIEST!

thank you and have a good day :)

Answer:

163/30

Step-by-step explanation:

4 3/5 in mixed number form would be 23/5

5/6 remains 5/6 as it is not greater than 1, therefore it cannot be simplified.

23/5 + 5/6

in order to add, we have to make the denominators alike. the least common multiple is 30. so we have to not just multiply the denominators by whatever results in 30, but also the numerators.

23 times 6 = 138

5 times 6 = 30

5 times 5 = 25

5 times 6 = 30

138/30 + 25/30

at this point, we can simply just add the numerators

163/30

i hope this helps

Answer:

x = -2, y = -4

Step-by-step explanation:

Take the first equation-   -2y = 2 - 3x
Arrange it first-
-3x + 2y = -2

Multiply is by 5 on both sides
5(-3x + 2y) = 5(-2)
-15x + 10y = -10

Take the second equation-    -5y = 10 - 5x
Arrange it-
-5x + 5y = -10

Multiply is by 2 on both sides
2(-5x + 5y) = 2(-10)
-10x + 10y = -20

Subtract second equation from the first one-

  -15x + 10y = -10
-  -10x + 10y = -20
= -5x = 10

-5x = 10
x = 10/(-5)
x = -2

Substitute the value of x in Equation 1
-2y = 2 - 3(-2)
-2y = 2 + 6
-2y = 8
y = 8/(-2)
y = -4

Hope it helps ;)

If m + 1 is an even integer, then 2m + 1 is an odd integer.

Even number: An even number is a number that is a multiple of 2. It can be said that any number that is completely divisible by 2 is an even number.

Odd number: Odd numbers are those numbers that are not completely divisible by 2.

let us understand by addition on different combinations of odd numbers and even numbers.

Odd number + Odd number = Even number

Even number + Even number = Even number

Even number + Odd number = Odd number

Odd number + Even number = Odd number

In subtraction

Even number - Even number = Even number

Even number - Odd number = Odd number

Odd number - Even number = Odd number

Odd number - Odd number = Even number

In multiplication

Even number × Even number = Even number

Even number × Odd number = Even number

Odd number × Odd number = Odd number

Given:

m + 1 is an even integer.

since alternate numbers are even.

Therefore, m must be an odd number.

If m is odd, then m - 1 is even.

2m is divisible by 2, so it is always an even number.

So,

2m - 2 is even.

2m + 1 is odd.

2m + 2 is even.

Since 2m + 1 is an odd number.

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Answer:

9 science books

Step-by-step explanation:

Step 1) 36 - 17 = 19

Step 2) 19 - 10 = 9

The correct decision in a hypothesis test when the data produces a t-statistic that is in the critical region is to reject the null hypothesis.

This is because a t-statics in the critical region indicates that the differences between the sample mean and the population mean are statistically significant. This means that the data indicates that the null hypothesis is wrong and that the alternative hypothesis is true. In a hypothesis test, the null hypothesis is what the researcher is trying to disprove. It is the general statement that suggests that there is no difference between the sample mean and the population mean. The alternative hypothesis is what the researcher is attempting to prove. It suggests that there is a difference between the sample mean and the population mean. Therefore, when the data produces a t-statistic that is in the critical region, it indicates that the alternative hypothesis is true. When a t-statistic is in the critical region, it means that the result is statistically significant. This means that the differences between the sample mean and the population mean are unlikely to have occurred by chance and that the alternative hypothesis is likely to be true. Therefore, when the data produces a t-statistic that is in the critical region, the correct decision is to reject the null hypothesis and accept the alternative hypothesis.

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The expression that is equivalent to x² +7x+12 ÷ x²+8x+15 is (x + 4) ÷ (x + 5)

From the question, we have the following parameters that can be used in our computation:

x² +7x+12

÷

x+8x+15

Express properly

So, we have

x² +7x+12 ÷ x²+8x+15

Factorize each expression

This gives

(x + 4)(x + 3) ÷ (x + 5)(x + 3)

Cancel out the common factor

(x + 4) ÷ (x + 5)

Hence, the expression is (x + 4) ÷ (x + 5)

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