(i) none of these ailments, 26
(ii) arthritis but neither of the other two ailments, 17
(iii) exactly one of these ailments, 102
(iv) arteriosclerosis and loss of hearing but not arthritis, 16
We can use a Venn diagram to solve this problem.
Let A, B, and C represent the events of having arthritis, arteriosclerosis, and loss of hearing, respectively. Then, the given information can be represented as:
A = 70
B = 60
C = 80
A ∩ B = 35
A ∩ C = 33
B ∩ C = 31
A ∩ B ∩ C = 15
Using these values, we can find the answers to the questions:
(i) The number of senior citizens with none of these ailments is the complement of the union of A, B, and C. That is:
n(A ∪ B ∪ C)' = n(S) - n(A ∪ B ∪ C)
= 200 - (70 + 60 + 80 - 35 - 33 - 31 + 15)
= 26
Therefore, 26 senior citizens had none of these ailments.
(ii) The number of senior citizens with arthritis but neither of the other two ailments is:
n(A) - n(A ∩ B) - n(A ∩ C) + n(A ∩ B ∩ C)' = 70 - 35 - 33 + 15
= 17
Therefore, 17 senior citizens had arthritis but neither of the other two ailments.
(iii) The number of senior citizens with exactly one of these ailments is the sum of the complements of the intersections of the events. That is:
n(A' ∩ B ∩ C') + n(A ∩ B' ∩ C') + n(A' ∩ B' ∩ C) = (200 - 60 - 31 - 15 - 33) + (200 - 70 - 31 - 15 - 33) + (200 - 70 - 60 - 15 - 35) = 102
Therefore, 102 senior citizens had exactly one of these ailments.
(iv) The number of senior citizens with arteriosclerosis and loss of hearing but not arthritis is:
n(B ∩ C) - n(A ∩ B ∩ C) = 31 - 15 = 16
Therefore, 16 senior citizens had arteriosclerosis and loss of hearing but not arthritis.
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5x +6y = 4
10x+12y = 8
What is the system of equation is it no solution, one solution, or infinitely many solutions?
The equation 5x + 6y = 4, 10x + 12y = 8 has infinitely many solution.
How to solve system of equation?System of equation can be solved using elimination method, substitution method and graphical method.
Therefore, let's solve the system of equation using elimination method.
5x + 6y = 4
10x + 12y = 8
multiply equation(i) by 2
Hence,
10x + 12y = 8
10x + 12y = 8
subtract the equations
0 = 0
Therefore, the equation has infinitely many solution.
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What is the area of this polygon?
Enter your answer in the box.
units?
Check the picture below.
so the polygon is really just a 5x7 rectangle with a triangle that has a base of 7 units(vertically) and a height of 2 units.
[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(5)(7)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(7)(2)}}\implies 35~~ + ~~7\implies \text{\LARGE 42}~units^2[/tex]
Find an equation of the line of symmetry of triangle ABC.
Answer:
The equation of the line of symmetry of triangle ABC is:
3x + 2y = 86Step-by-step explanation:
The line of symmetry of an isosceles triangle bisects the vertex angle (the angle opposite the base) and is perpendicular to the base of the triangle.
As AB = AC, then angle A is the vertex angle of the isosceles triangle ABC.
If B and C lie on the line with equation 3y = 2x + 12, then the line of symmetry is the line that is perpendicular to this line and passes through A (4, 37).
Rearrange the given equation 3y = 2x + 12 to slope-intercept form by dividing both sides by 3:
[tex]\implies y=\dfrac{2}{3}x+4[/tex]
Perpendicular lines have slopes that are negative reciprocals of one another. Therefore, the slope of the perpendicular line is -³/₂.
Substitute the found slope and point A (4, 37) into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-37=-\dfrac{3}{2}(x-4)[/tex]
Rearrange the equation to standard form:
[tex]\implies 2y-74=-3(x-4)[/tex]
[tex]\implies 2y-74=-3x+12[/tex]
[tex]\implies 3x+2y-74=12[/tex]
[tex]\implies 3x+2y=86[/tex]
Therefore, the equation of the line of symmetry of triangle ABC is:
3x + 2y = 86A 13-foot ladder is leaning up against a building. The top of the ladder reaches the wall at a height of 12 feet. How far is the
bottom of the ladder from the building? Find the angle (2B) that the ladder makes with the ground?
A
12
C
building
13
ladder
X
ground
B
How far is the ladder from the building? Find x = ?
Keep the results to the nearest whole number.
feet
Find the angle that the ladder makes with the ground? LB =
Keep the results to the nearest whole number.
The angle that the ladder makes with the ground is ∠B = 67.38°.
The distance between the ladder from the building is 5 feet.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Given that a 13-foot ladder is placed up against a wall.
The ladder's top touches the wall at a height of 12 feet.
As per the given question, we have the right triangle ΔABC
Using sine ratio to find angle ∠B as:
sin ∠B = AC/ AB
sin ∠B = 12/13
∠B = sin ⁻¹(12/13)
∠B = 67.38°
Now, using Pythagoras's theorem to find distance x as:
AC² + BC² = AB²
12² + x² = 13²
144 + x² = 169
x² = 169 - 144
x² = 25
x = 5
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Algebra tiles??
Please help!!
Answer:
(-x+2)(2x+1) — first option
Step-by-step explanation:
The rectangles represent an x, red means negative and yellow is positive.
The squares represent a unit (the number 1).
The diagram attached below demonstrates how this works.
Basically the top row of this tile equation is (-x + 2)And the column is (2x+1).
Expanding this makes -2x²+3x+2
Determine whether segments with lengths of 29, 19, and 29 form a triangle. If so, classify the triangle as acute, right, or obtuse.
Answer:
if the angle has the arrow on top pointing straight up thats a right angle if it is leaning towards the left instead it is obtuse and if is getting closer to the right side it is acute.
Step-by-step explanation:
i can't tell you anything else if there is no picture to base this question.
PLEASE SHOW UR WORK ANSWER QUICK
The profit that they will make if they have 24 dogs for adoption is given as follows:
$160.
How to obtain the profit?The profit is obtained with the subtraction of the revenue by the costs.
The revenue and the costs for this problem are obtained as follows:
Revenue: $45 for each of the 24 dogs adopted.Costs: $920 on supplies.Hence the profit made is obtained as follows:
Profit = 45 x 24 - 920
Profit = $160.
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the tortoise and the hare are running a 1 km race. after running comfortably for 7 s, the hare is so far ahead that he decides to take a nap under a tree, 100 m away from the finish line. if the tortoise is moving constantly at a speed of 0.27 m/s, and the maximum speed of the hare is 15 m/s, how long can the hare afford to nap if he does not want to lose the race?
The hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.
We can use the time it takes the hare to run 100 m to determine how long he can afford to nap.
First, let's find the time it takes the hare to run the 100 m:
t = d / v
Where t is the time, d is the distance, and v is the velocity (speed) of the hare.
t = 100 m / 15 m/s
t = 6.67 s
Next, let's find the time it takes the tortoise to run 1 km (1000 m):
t = d / v
Where t is the time, d is the distance, and v is the velocity (speed) of the tortoise.
t = 1000 m / 0.27 m/s
t = 3700 s
So, the time it takes the tortoise to run the race is 3700 s. The time it takes the hare to run the first 900 m is 7 s. Therefore, the time the hare has left to nap is:
3700 s - 7 s = 3693 s
And the time it takes the hare to run the last 100 m is 6.67 s. Therefore, the hare can afford to nap for:
3693 s - 6.67 s = 3686.33 s
So, the hare can afford to nap for approximately 3686.33 seconds if he does not want to lose the race.
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If 3 times a certain number is increased by 4 the result is 28. What is the number?
Answer:
8
Step-by-step explanation:
8x3 = 24
24 + 4 = 28
monique is 2 years older than vanessa. the sum of their ages is 32.let v represent vanessas age.which of the following equations can be used to find vanessas age?
a.v+2=32
b.2v -2=32
c.v+(v-2)=32
d.v+(v+2)=32
The correct option is a. The equation used to find Vanessa's age is v + 2 = 32.
What is an equation?A mathematical statement known as an equation utilises the equals sign to demonstrate the equality of two expressions. It may be used to address a variety of issues and can contain both numbers and variables. Algebraic operations including addition, subtraction, multiplication, division, and exponentiation are frequently used in equations.
In the given question, Vanessa's age may be calculated using the equation a. v+2=32. This equation shows that Vanessa's age plus 2 equals 32, implying that Vanessa's age is 30. We may solve this equation by removing 2 from both sides, yielding v=30. This equation is valid for determining Vanessa's age because it specifies that Vanessa's age plus Monique's age equals 32.
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megan wants to test her assumption on the amount of sleep students are getting. she decides to focus her efforts on examining if students are getting less than eight hours of sleep. what should megan state for the null hypothesis and alternative hypothesis? a.) null hypothesis: alternative hypothesis: b.) null hypothesis: alternative hypothesis: c.) null hypothesis: alternative hypothesis: d.) null hypothesis: alternative hypothesis:
To state the null hypothesis and alternative hypothesis for Megan's test, we need to know what type of data she will be collecting and what type of test she will be conducting.
Assuming she will be collecting data on the number of hours of sleep students are getting and conducting a one-tailed hypothesis test, the following are possible null and alternative hypotheses:
a.) Null hypothesis: The average amount of sleep students are getting is equal to or greater than eight hours per night.
Alternative hypothesis: The average amount of sleep students are getting is less than eight hours per night.
b.) Null hypothesis: Less than or equal to 50% of students are getting less than eight hours of sleep per night.
Alternative hypothesis: More than 50% of students are getting less than eight hours of sleep per night.
c.) Null hypothesis: There is no difference in the proportion of students getting less than eight hours of sleep between two groups (e.g., males vs. females, freshmen vs. seniors, etc.).
Alternative hypothesis: There is a difference in the proportion of students getting less than eight hours of sleep between two groups.
d.) Null hypothesis: The number of students getting less than eight hours of sleep is equal to or greater than a certain value (e.g., 30%).
Alternative hypothesis: The number of students getting less than eight hours of sleep is less than the specified value.
Note that in each case, the null hypothesis represents the status quo or the default assumption, while the alternative hypothesis represents Megan's research question or hypothesis. The choice of null and alternative hypotheses depends on the research question, the data being collected, and the type of hypothesis test being conducted.
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HELPP PLSSS
Factor the polynomial.
x²+2x² +14x+7x²
Answer:
2x(5x+7)
Step-by-step explanation:
[tex]x^2+2x^2+14x+7x^2\\=10x^2+14x\\=2x(5x+7)[/tex]
the primary tool or measure for determining whether the assumed regression model is appropriate is .
The primary tool or measure for determining whether the assumed regression model is appropriate is the residual plot.
A residual plot is a graph that shows the residuals, or the differences between the observed values and the predicted values from the regression model, plotted against the predictor variable(s). If the residuals are randomly scattered around zero, with no discernible pattern, then the regression model is a good fit for the data.
However, if there is a pattern in the residuals, such as a curved or U-shaped relationship, then the regression model may not be appropriate and a different model may need to be considered.
In addition to the residual plot, other measures such as the coefficient of determination (R-squared), the p-values of the regression coefficients, and the normality of the residuals can also be used to evaluate the goodness of fit of a regression model.
However, the residual plot is often considered the primary tool for assessing the adequacy of a regression model.
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(Right answers only. please help thanks)
A quilter created the following shape to use in a block for a new quilt.
A six-sided figure with a large base of 10 and three-fifths inches. The side to the right of the base is 6 inches. The small side parallel to the base is 4 and one-fifth inches. There are two sides that form a point at a right angle. The smaller is 4 inches, and the larger is 5 inches.
What is the area of the shape for the quilt block?
73 3/5 in
41 4/5 in
83 3/5 in
147 1/5 in
Answer: 83 3/5
Step-by-step explanation:
hope this helps !! :3
the days to maturity for a sample of five money market funds are shown here. the dollar amounts invested in the funds are provided. days to maturitydollar value ($ millions) 1515 1110 725 515 410 use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds. round your answer to decimal places. days
The mean number of days to maturity for dollars invested in these five money market funds is approximately 8.95 days.
To calculate the weighted mean of the days to maturity, we need to multiply each value of days to maturity by its corresponding dollar value, sum the products, and divide the result by the total dollar value.
The calculation for the weighted mean is as follows:
Weighted Mean = (D1 x V1 + D2 x V2 + D3 x V3 + D4 x V4 + D5 x V5) / (V1 + V2 + V3 + V4 + V5)
where D represents the days to maturity and V represents the dollar value.
Using the given values, we can plug them into the formula and get:
Weighted Mean = (15 x 15 + 11 x 10 + 7 x 25 + 5 x 15 + 4 x 10) / (15 + 10 + 25 + 15 + 10)
Weighted Mean = 8.95 (rounded to two decimal places)
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data with 860 observations are drawn from a bell-shaped distribution with a mean of 76 and a standard deviation of 18. approximately how many observations are more than 112? (round your answer to the nearest whole number.)
In the given case where 860 observations are drawn from a bell-shaped distribution, there are 2 observations of more than 112.
Total number of observations = 860
Mean of the observations = 76
Standard deviation = 18
The amount of standard deviations by which the value of a raw score differs from or differs above the mean value of what is observed or measured is known as the z score or standard score in the z test. The z-score calculates how far an X-score deviates from the mean by standard deviations. Calculating the observations utilizing the Z- score -
Z = X - u/a
Calculating the observations -
Where X = 112 u = 76 and a = 18
Z = 112 - 76/18
= 36/18
= 2
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Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.
The average rate of change of f(x) over the interval 3≤x≤4 is 15
What is the average rate of change of f(x) over the intervalFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table, we have
f(3) = -4
f(4) = 11
The average rate is then calculated as
Average rate = [f(4) - f(3)]/[4 - 3]
Substitute the known values in the above equation, so, we have the following representation
Average rate = (11 + 4)/(4 - 3)
Evaluate
Average rate = 15
Hence, the average rate is 15
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Complete question
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3\le x \le 43≤x≤4.
X f(x)
3 -4
4 11
5 8
6 10
7 11
8 14
There are approximately 1. 06 quarts per liter. There are 4 quarts per gallon. If gasoline cost $0. 50 per liter, how much does gasoline cost per gallon?
A. $1. 42/gal
B. $1. 75/gal
C. $1. 89/gal
D. $2. 12/gal
E. $4. 24/gal
Answer:
$1.89/gal
Step-by-step explanation:
the mariana trench is about 11km deep. mount everest is about 29,000 ft high. what is the total height change from the top of mount everest to the bottom of the mariana trench, expressed in miles?
Using unit conversions the total height change from the top of mount Everest to the bottom of the Mariana trench is 12.3 miles
We know that 1 km = 0.62136 miles and 1 foot = 0.000189 miles
Depth of Mariana Trench (d) = 11 km = 11 × 0.62136
= 6.835 miles
Height of Mount Everest (h) = 29000 ft = 29000 × 0.000189
= 5.492 miles
Therefore the total height difference top of Mount Everest and to bottom of the Mariana Trench is given by
H = Depth of Mariana Trench + Height of Mount Everest
H = d + h
H = 6.835 miles + 5.492 miles
H = 12.327 miles
H = 12.3 miles
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2. Two observers are 600 ft apart on opposite sides of a flagpole. The angles of elevation from the
observers to the top of the pole are 19 and 21°. Find the height of the flagpole. Round to the nearest
foot.
The height of the flagpole is 110 feet.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
From the figure,
tan 19 = f/x
tan 21 = f/(600 - x)
Now,
tan 16 x = tan 21 x (600 - x)
0.34x = 0.38 x 600 - 0.38x
0.34x = 230 - 0.38x
0.34x + 0.38x = 230
0.72x = 230
x = 319
Now,
tan 19 = f/319
0.34 x 319 = f
f = 109.8
f = 110 feet
Thus,
110 feet is the height of the flagpole.
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what is 3 1/2x - 5 1/2x,x=2/5
Answer:
[tex]-\dfrac{4}{5}[/tex]
Step-by-step explanation:
We have the following expression
[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x[/tex]
and asked to evaluate this expression at [tex]\[x = {2\over\displaystyle 5\][/tex]
First convert [tex]3 \; \dfrac{1}{2}[/tex] and [tex]5 \; \dfrac{1}{2}[/tex] to mixed fractions
[tex]3 \; \dfrac{1}{2} = \dfrac{3 \times 2 + 1}{2} = \dfrac{7}{2}\\[/tex]
[tex]5 \; \dfrac{1}{2} = \dfrac{5 \times 2 + 1}{2} = \dfrac{11}{2}[/tex]
Therefore
[tex]3 \;\dfrac{1}{2} x - 5\;\dfrac{1}{2}x\\\\= \dfrac{7}{2}x - \dfrac{11}{2}x\\\\= \dfrac{7 - 11}{2} x\\\\= -\dfrac{4}{2}x \\\\= -2x\\\\[/tex]
[tex]\mathrm{For \;x =\dfrac{2}{5}},\\\\= -2x \\= - 2 \times \dfrac{2}{5}\\\\= -\dfrac{4}{5}[/tex]
I need help with this please
Answer:
see explanation
Step-by-step explanation:
given sinΘ = - [tex]\frac{3}{5}[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]
the negative sign indicates sinΘ is in the third quadrant where sinΘ < 0
this is a 3- 4- 5 right triangle with opposite = 3 and hypotenuse = 5
then the adjacent side = 4
cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = - [tex]\frac{4}{5}[/tex] ( since cosΘ < 0 in third quadrant )
secΘ = [tex]\frac{1}{cos0}[/tex] = [tex]\frac{1}{-\frac{4}{5} }[/tex] = - [tex]\frac{5}{4}[/tex]
tanΘ
= [tex]\frac{sin0}{cos0}[/tex]
= [tex]\frac{-\frac{3}{5} }{-\frac{4}{5} }[/tex]
= - [tex]\frac{3}{5}[/tex] × - [tex]\frac{5}{4}[/tex]
= [tex]\frac{3}{4}[/tex]
A dietician recommends 48 grams of protein each day for his patient. At the end of the day, the patient has only eaten 40 grams of protein. What percent of her daily intake has the patient eaten?
Answer:
83%
Step-by-step explanation:
To find the percentage divide 40 by 48
40/48 = 0.83333333333333
Round to 0.83
Multiply by 100
The patient has only eaten 83% of her daily intake.
hospital records show that 12% of all patients are admitted for heart disease, 16% are admitted for cancer (oncology) treatment, and 4% receive both coronary and oncology care. what is the probability that a randomly selected patient is admitted for coronary care, oncology or both? (note that heart disease is a coronary care issue.)
The probability of randomly selected patient selected for coronary, oncology or both is equal to P( H∪C ) = 0.24.
Let patient admitted with heart disease represented by P(H)
P(H) = 12%
= 0.12
And patient admitted for cancer disease represented by P(C)
P(H) = 16%
= 0.16
Percent of patient received both coronary and oncology = 4%
P( H∩C ) = 0.04
Probability of randomly selected patient admitted for coronary, oncology or both is :
P( H∪C ) = P(H) + P(C) - P(H∩C )
⇒P( H∪C ) = 0.12 + 0.16 - 0.04
⇒ P( H∪C ) = 0.24
Therefore, the probability of randomly selected patient getting treatment for coronary, oncology or both is given by P( H∪C ) = 0.24.
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what is the slope of the line that contains the points (-2,6) and (6,-3)?
PLEASE SHOW WORK
Answer: [tex]-\frac{9}{8}[/tex]
Step-by-step explanation:
If you are given two points of a line, the slope is defined as rise/run. Rise is the difference in y coordinates, (think about it, going UP is RISING), and Run is the difference in x coordinates, (again its pretty intuitive.)
So Slope = [tex]\frac{y_{2} - y_{1}}{x_{2}-x_{1}}[/tex]
This can be calculated with the coordinates of the two points, (order wont matter youll get the same answer).
Slope = (-3-6)/(6-(-2)) = -9/8
OR, (going the other way)
Slope = (6-(-3))/(-2-6) = 9/-8 = -9/8
Easy!
a college student is preparing a course schedule of four classes for the next semester. the student can choose from the open sections shown in the table. (a) find the number of possible schedules that the student can create from the offerings. (b) find the number of possible schedules that the student can create from the offerings if two of the math 100 sections are closed. (c) find the number of possible schedules that the student can create from the offerings if two of the math 100 sections and four of the english 105 sections are closed.
(a) The number of possible schedules that the student can create from the offerings is 96.
(b) the number of possible schedules that the student can create from the offerings if two of the math 100 sections are closed is 48.
(c) the number of possible schedules that the student can create from the offerings if two of the math 100 sections and four of the English 105 sections are closed is 4.
(a) To find the total number of possible schedules, we need to multiply the number of choices for each class:
Number of schedules = 4 x 2 x 3 x 4 = 96
So, there are 96 possible schedules that the student can create from the offerings.
(b) If two of the math 100 sections are closed, then there are only two choices for that class. So, we have:
Number of schedules = 2 x 2 x 3 x 4 = 48
So, there are 48 possible schedules that the student can create from the offerings with two of the math 100 sections closed.
(c) If two of the math 100 sections and four of the English 105 sections are closed, then there are only two choices for math 100 and one choice for English 105. So, we have:
Number of schedules = 2 x 2 x 1 x 1 = 4
So, there are 4 possible schedules that the student can create from the offerings with two of the math 100 sections and four of the English 105 sections closed.
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consider two boxes, one containing 1 black and 1 white marble, and other 2 black and 1 white marble. a box is selected at random, and a marble is drawn from it at random. what is the probability that the marble is black? what is the probability that the first box was the one selected given that the marble is white?
The probability that the first box was the one selected given that the marble is white is [tex]\frac{7}{12}[/tex] .
Probability is the likelihood that an event will occur.
The likelihood of an occurrence A provided that an earlier event B has already happened is known as conditional probability.
the two boxes are marked as B1, B2
Number of black balls: 1
Number of white balls: 1
Number of black balls in the box: 2,
Number of white balls: 1.
B and W should stand for black and white marble.
Therefore, the likelihood that either box will be selected is [tex]\frac{1}{2}[/tex]
Probability of selecting a black ball from a box: [tex]\frac{1}{2}[/tex]
Probability of selecting a black ball from a box: [tex]\frac{2}{3}[/tex]
To determine: the likelihood that the marble is black.
Solution:
The likelihood that the marble being black is equal to
[tex]\frac{1}{2} (\frac{1}{2} ) + \frac{1}{2} (\frac{2}{3} )\\= \frac{7}{12}[/tex]
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Simplify Fully (Negative powers)
Answer:
[tex]\frac{y^2}{4x^5}[/tex]
Step-by-step explanation:
Used Exponents Properties :
[tex]\blacksquare \left( a\times b\right)^{n} =a^{n}\times b^{n}\\\blacksquare \left( a^{n}\right)^{m} =a^{n\times m}\\\blacksquare \left( \frac{a}{b} \right)^{n} =\frac{a^{n}}{b^{n}}[/tex]
==========================
[tex]\begin{aligned}\left(\frac{256 \times x^{20}}{y^8}\right)^{-\frac{1}{4}} & =\left(\frac{y^8}{2^8 \times x^{20}}\right)^{\frac{1}{4}} \\& =\frac{\left(y^8\right)^{\frac{1}{4}}}{\left(2^8 \times x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{8 \times \frac{1}{4}}}{\left(2^8\right)^{\frac{1}{4}} \times\left(x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{\frac{8}{4}}}{2^{\frac{8}{4}} \times x^{\frac{20}{4}}} \\& =\frac{y^2}{2^2 x^5}\\& =\frac{y^2}{4 x^5}\end{aligned}[/tex]
Use the Distributive Property to solve each equation.
a. −1/2(b−6)= 5
b. 0.4(x−0.45)= 9.2
c. −4(p−212)=44
please help
The required answers are
a) b = -4
b) x = 23.45
c) p = 201
Distributive Property:The distributive property implies that multiplying a number by the sum of two or more addends yields the same result as dividing the multiplier, multiplying each addend individually, and combining the products . It can be given as,
a (b+c) = d
[tex](a*b) + (a*c) = d[/tex]
Now in the given question,
a) −1/2(b−6)= 5
by distributive property , we have
[tex](\frac{-1}{2} *b)-(\frac{-1}{2}*6 )=5\\\frac{-1}{2}b+3=5\\\frac{-1}{2}b=2\\b=-4[/tex]
b) 0.4(x−0.45)= 9.2
by distributive property , we have
0.4x - 0.4(0.45) =9.2
0.4x -0.18 = 9.2
0.4x = 9.38
x = 23.45
c) −4(p−212)=44
by distributive property , we have
-4p +4 (212) = 44
-4p + 848 =44
-4p = 44 - 848
-4p = -804
p = 201
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How many 3-letter words can we make from the letters A, B, C, and D, if we are allowed to repeat letters, and we must use the letter A at least once?
Answer:
37
Step-by-step explanation:
AAA 1 way
AAB, AAC, AAD 3 ways each 3*3=9 ways
ABB, ACC, ADD 3 ways each 3*3=9 ways
ABC, ABD, ACD 3*2=6 ways each 3*6=18ways
1+9+9+18 = 37 ways
