Which represents the inverse of the function f(x) = 4x? a) h(x) = x + 4 b) h(x) = x – 4 c) h(x) = x d) h(x) = x witch is right
which of the following is a Pythagorean triple?
A. 3,4,6
B.7,25,26
C.15,21,25
D.9,40,41
Henry wanted to make two bakery items. One recipe called for 1 1/4 cup of sugar and the other for 2/3 cup of sugar. How much sugar does he need?
A. 1 11/12
B. 1 1/12
C. 1 3/7
D. 1 1/4
£1800 is invested at4% compound interest per year.
How many years will it take for the investment to be worth £2000?
A homemade lip balm consists of coconut oil and beeswax. Coconut oil costs $0.50 per ounce and beeswax costs $2.00 per ounce. If 6 ounces of coconut oil and 5 ounces of beeswax are used to create the lip balm mixture, which values represent a and b in the table?
what does a and b equal
a = $
b = $
Let
a--------> the total cost in dollars of [tex]6[/tex] ounces of coconut oil
b--------> the total cost in dollars of [tex]5[/tex] ounces of beeswax
we know that
[tex]a=0.50 \frac{\$}{ounce}*6=\$3[/tex]
[tex]b=2.00 \frac{\$}{ounce}*5=\$10[/tex]
therefore
the answer is
the total cost in dollars of [tex]6[/tex] ounces of coconut oil is [tex]a=\$3[/tex]
the total cost in dollars of [tex]5[/tex] ounces ofbeeswax is [tex]b=\$10[/tex]
Six different written driving tests are administered by the Motor Vehicle Department. One of these six tests is selected at random for each applicant for a driver's license. A group consisting of two women and three men apply for a license. (Round your answers to three decimal places.)
(a) What is the probability that exactly two of the five will take the same test?
(b) What is the probability that the two women will take the same test?
To find the probability that exactly two of the five will take the same test, we use combinations. The probability is 2/3 or 0.667. To find the probability that the two women will take the same test, we use combinations. The probability is 1/2 or 0.500.
To find the probability that exactly two of the five will take the same test, we can use the concept of combinations. There are six different tests, and we need to choose two of them to be taken by two people. The total number of ways to select two tests out of six is given by the combination formula C(6,2) = 6!/(2!(6-2)!) = 15. Now, for each of these two selected tests, there are two people (either two men or two women) who can take the test, resulting in a total of two possibilities. Therefore, the number of favorable outcomes is 2 * 15 = 30. Finally, the probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is 6!/(2!3!) = 15. So the probability is 30/15 = 2/3 or 0.667 (rounded to three decimal places).
To find the probability that the two women will take the same test, we can use similar reasoning. There are six different tests, and we need to choose one of them to be taken by both women. The total number of ways to choose one test out of six is given by the combination formula C(6,1) = 6!/1!(6-1)! = 6. Now, for the chosen test, there are three possible ways both women can take it, since they can be the first two applicants, the last two applicants, or the middle two applicants. Therefore, the number of favorable outcomes is 3. The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes, which is also 6. So the probability is 3/6 = 1/2 or 0.500 (rounded to three decimal places).
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Final answer:
The probability that exactly two of the five will take the same test is 0.00463. The probability that the two women will take the same test is 1.167.
Explanation:
To find the probability that exactly two of the five will take the same test, we can use combinations. There are 6 different tests and we want to select 2 of them for the same test. Since order doesn't matter, we can use combinations. The number of ways to choose 2 tests out of 6 is 6 choose 2 = 15.
Now, for each pair of tests, we have 5 people who can take those tests. The probability that exactly 2 of the five will take the same test is the probability that exactly 2 people are randomly assigned to the same test out of the 5 people. The total number of possible outcomes is 6^5 since each person has 6 choices for which test to take, and there are 5 people.
So, the probability that exactly two of the five will take the same test is 15/6^5, which is approximately 0.00463.
To find the probability that the two women will take the same test, we consider the different possibilities. The two women can take the same test out of the 6 tests, or they can take different tests.
If they take the same test, there are 5 possible tests for them to choose from. The probability of this happening is 5/6.
If they take different tests, there are 5 possible tests for each of them to choose from. The probability of this happening is (5/6) * (4/5) = 2/3.
Therefore, the probability that the two women will take the same test is (5/6) + (2/3) = 7/6, which is approximately 1.167.
280 divided by 30 what is it
The division yields to quotient is 9, and there is 10 as remainder
We have to divide 280 by 30.
So, the division performed as
30 | 280 | 9
270
-______
10
So, the quotient is 9, and there is 10 as remainder.
So, 280 divided by 30 is equal to 9.33 (rounded to two decimal places) or simply 9.
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What is the vertex of the absolute value function defined by ƒ(x) = |x - 7| + 1?
(7,1)
(-7,-1)
(-7,1)
(7,-1)
Answer: [ 7,1 ]
Step-by-step explanation:
this is the answer on odyssey ware.
the total amount of degrees in the center is 360 degrees if all five vertex angles meeting the center are congrent what is the measure of a base angle of one of the triangles
A) 54 degrees
B) 72 degrees
C) 108 degrees
D) 144 degrees
Answer:
(B) 72°
Step-by-step explanation:
prove:
when xz= yz then x=y if z is not equal to zero
If A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4) form two line segments, AB and CD , which of these conditions needs to be met to prove that AB is perpendicular to CD?
see attachment for choices
Answer:
[tex]\frac{y_4-y_3}{x_4-x_3}\times \frac{y_2-y_1}{x_2-x_1}=-1[/tex]
Step-by-step explanation:
We know that,
If two line segments are perpendicular then the product of their slope is equal to -1,
Also, the slope of a line segment having the end points [tex](x_n,y_n)[/tex] and [tex](x_m,y_m)[/tex] is,
[tex]m=\frac{y_m-y_n}{x_m-x_n}[/tex]
So, the slope of line segment AB having end points [tex]A(x_1,y_1)[/tex] and [tex]B(x_2,y_2)[/tex] is,
[tex]m_1=\frac{y_2-y_1}{x_2-x_1}[/tex]
Similarly, the slope of line segment CD having end points [tex]C(x_3,y_3)[/tex] and [tex](x_4,y_4)[/tex] is,
[tex]m_2=\frac{y_4-y_3}{x_4-x_3}[/tex]
Hence, by the above property of perpendicular line segments ,
If AB and CD are perpendicular then,
[tex]m_1\times m_2=-1[/tex]
[tex]\implies \frac{y_4-y_3}{x_4-x_3}\times \frac{y_2-y_1}{x_2-x_1}=-1[/tex]
Third option is correct.
Find the solution to the equations.
3x - y = -4
x + y = 0
(0, 0)
(-1, 1)
(1, -1)
HELP ASAP!!!
The markup on appliances at Tom’s store is 50%. If the wholesale price of a dishwasher is $380, what price will Tom list when selling the dishwasher?
A. $570
B. $665
C. $760
D. $950
ABCD ~ WXYZ. AD=12, DC=3 AND WZ=35. FIND YZ.
THE FIGURES ARE NOT DRAWN TO SCALE.
The unknown length YZ can be found through the ratios of corresponding sides in similar figures ABCD and WXYZ. Given AD=12, DC=3, WZ=35, the equation 3/YZ = 12/35 is formed. Solving for YZ, we find that YZ is 8.75.
Explanation:In the given question, ABCD and WXYZ are similar figures which mean the ratio of corresponding sides are equal. So, the ratio AD/WZ equals to the ratio DC/YZ. Given, AD=12, DC=3 and WZ=35. The length of YZ can be found by cross multiplying these ratios.
So, DC/YZ = AD/WZ.
By substituting the given values:
3/YZ = 12/35.
To find YZ, we simply cross-multiply and solve for YZ:
3 × 35 = 12 × YZ,
Hence, YZ = (3 × 35) / 12, which is 8.75 units.
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simplify 8a+4b-3a+5b
The simplified form of the expression [tex]8a+4b-3a+5b[/tex] is [tex]\boxed{5a+9b}[/tex].
Further explanation:
The given expression is [tex]8a+4b-3a+5b[/tex].
The given expression consists of [tex]2[/tex] different variables [tex]a[/tex] and [tex]b[/tex]. These variables can take any values since, its value is not fixed.
An algebraic expressions are formed if different variables and are added, subtracted, multiplied and divided.
The given expression is obtained when the variable [tex]a[/tex] and variable [tex]b[/tex] is added and subtracted with multiplication with different integers.
In the given expression there are [tex]4[/tex] terms with each term having different coefficients.
Like terms in the given expression are those whose algebraic factors are same that is [tex]8a[/tex] and [tex]-3a[/tex] are like terms and [tex]4b[/tex] and [tex]5b[/tex] are like terms.
The given expression is a binomial since, it have two unlike terms.
To simplify the given expression first we have to identify the like and unlike terms.
The like terms are [tex]8a[/tex] and [tex]-3a[/tex] and other set of like terms are [tex]4b[/tex] and [tex]5b[/tex]
Since, [tex]a[/tex] and [tex]b[/tex] are variable and they are numbers they can be added or subtracted using distributive property.
[tex]8a[/tex] and [tex]-3a[/tex] are subtracted as follows:
[tex]\begin{aligned}8a-3b&=(8\cdot a)-(3\cdot a)\\&=(8-3)\cdot a\\&=5\cdot a\\&=5a\end{aligned}[/tex]
[tex]4b[/tex] and [tex]5b[/tex] are added as follows:
[tex]\begin{aligned}4b+5b&=(4\cdot b)+(5\cdot b)\\&=(4+5)\cdot b\\&=9\cdot b\\&=9b\end{aligned}[/tex]
Therefore, simplified form of the given expression is [tex]5a+9b[/tex] since both are positive terms.
Thus, the simplified form of the expression [tex]8a+4b-3a+5b[/tex] is [tex]\boxed{5a+9b}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Algebraic expressions
Keywords: Simplify, 8a+4b-3a+5b, expression, 5a+9b, terms, coefficients, like, unlike, addition, subtraction, variables, values, distributive property, like terms, unlike terms.
what is an acrostic poem for the word triangle?
Final answer:
An acrostic poem for the word 'triangle' is a creative way to convey various attributes of the geometric shape or to create a poem with each line starting with the corresponding letter. The poem can be directly related to the properties of a triangle or more abstract.
Explanation:
An acrostic poem uses the first letter of each line to spell out a word vertically. For the word 'triangle', an acrostic poem might be a creative way to describe the characteristics of a triangle, or it could be abstract, using each letter to begin a line that doesn't necessarily relate to the shape but instead creates a coherent poem.
Here is an example of an acrostic poem for the word 'triangle':
Three sides enclosing space,
Reminder of structure and base,
In geometry, an essential grace,
Angles acute, obtuse, or right,
Nestled within, points of light,
Guiding principles of design,
Lines intersect by plan divine,
Eternally, three lines combine.
Remember, while writing an acrostic for 'triangle', you may also use the opportunity to incorporate into your poem mnemonics for the relationships between the sides and angles of a right triangle, such as 'SOHCAHTOA', or explore the figurative and metaphorical implications of the shape as referenced in literary examples or the sciences.
Two groups of students were asked how far they lived from their school. The table below shows the distances in miles:
Group A (distance in miles)1 1.589.26.84.54.82.50.76
Group B (distance in miles)22.53.231.31.82.431.51.8
Which statement best compares the mean distances for the two groups?
A. It is equal for Group A and Group B.
B. It is greater for Group B than Group A.
C. Its value for group A is double the value for Group B.
D. Its value for group B is three times the value for Group A.
Which of the following represents the graph of f(x) = 2x + 2? i will give a medal if you help cooperatively
A scientist had 3/ 5 liter of solution. He used 7/ 12 of the solution for an experiment.
How many liters of solution did the scientist use for the experiment
The only part of the United States explored by Russia was the:
A : Hudson River
B : Southwest and Mexico
C : Mississippi River
D : Northwest coastline
Answer:
d
Step-by-step explanation:
d
Which point satisfies the equation 2x+3y=8? A) (-1,3) B) (2,2) C) (-2,4) D) (1,4)
The point that satisfies the equation 2x+3y=8 is (1,4).
Explanation:To find the point that satisfies the equation 2x + 3y = 8, we can substitute the x and y values from each option into the equation and see which option makes the equation true.
Let's try option A, (-1,3): 2(-1) + 3(3) = -2 + 9 = 7, which is not equal to 8.
Continuing this process for options B, C, and D, we find that the point (1,4) satisfies the equation 2x + 3y = 8.
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0.66 = 6/10
66/100
2/3
The table shows the total number of hamburgers and hot dogs sold at a food stand at a local fair on two separate days. It also shows the dollar amount taken in each day.
Hamburgers Hot Dogs Total
Day 1 200 150 $1,450
Day 2 200 250 $1,750
What is the cost of a hamburger and the cost of a hot dog?
Enter your answers in the boxes.
Hamburger: $
Hot dog: $
the temperature was 8 below zero in the morning and dropped 12 degrees during the afternoon. what was the temperature late in the afternoon
The temperature was -20 in the afternoon.
What are arithmetical operations?The arithmetic operators are addition, subtraction, multiplication and division. The arithmetic operators are applied between two or more numbers or quantities.
Given that, the temperature was 8 below zero in the morning and dropped 12 degrees during the afternoon.
We need to find the temperature late in the afternoon.
We know,
8 below zero is -8 degrees.
Now it is saying that the temperature dropped by 12 degrees,
Therefore,
-8 -12
-8 + (-12) = -20
Hence the temperature was -20 in the afternoon.
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15 percent of 45.4 is what?
the population of a bacteria culture doubles in number every 12 minutes. the ratio of the number of bacteria at the end of 1 hour to the number of bacteria at the beginning of the hour is? ...?
Answer:
32
Step-by-step explanation:
Let X be the number of bacteria at the initial time.
At 12 minutes = 2 X
At 24 minutes = 4X
At 36 minutes = 8X
At 48 minutes = 16X
At 60 minutes = 32X
The ratio between the final and the initial instant will be: 32X / X = 32
60 minutes is 20% of ? minute s
What is an equivalent decimal for 29/30?
For the function f(x)=x+5, what is the ordered pair for the point on the graph when x=4w?
Answer:
(4w, 4w + 5)
Step-by-step explanation:
One pipe can fill a swimming pool in 8 hours. Another pipe takes 12 hours. How long will it take to fill the pool if both pipes are used simultaneously?