Answer:
162, 163, and 164.
Step-by-step explanation:
Here we will use algebra to find three consecutive integers whose sum is 489. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 489. Therefore, you can write the equation as follows:
(X) + (X + 1) + (X + 2) = 489
To solve for X, you first add the integers together and the X variables together. Then you subtract three from each side, followed by dividing by 3 on each side. Here is the work to show our math:
X + X + 1 + X + 2 = 489
3X + 3 = 489
3X + 3 - 3 = 489 - 3
3X = 486
3X/3 = 486/3
X = 162
Which means that the first number is 162, the second number is 162 + 1 and the third number is 162 + 2. Therefore, three consecutive integers that add up to 489 are 162, 163, and 164.
162 + 163 + 164 = 489
We know our answer is correct because 162 + 163 + 164 equals 489 as displayed above.
Answer:
161, 163, 165
Step-by-step explanation:
x + x+2 + x +4 =489.
This is how we calculate three consecutive odd integers!
Combine like terms:
3x+6=489
3x=483
x=161
Three numbers are:
161, 161+2, 161+4.
161, 163, 165
Write each phrase as a mathematical expression.
The quotient of 8 more than the radius, r, and 4
Answer: (r+8)/4
Step-by-step explanation:
Not much really to explain...
y is directly proportional to x and inversely proportional to the square of w. Give the equation:
Answer: y=kx/w^2
Step-by-step explanation:
y is directly proportional to x
y∝x
y=kx
y inversely proportional to the square of w.
y ∝ (1/(w)^2)
y=k/w^2
y=kx/w^2
Evaluate a=5 and y= -7 for y-2a
Answer: -17
Step-by-step explanation:
y - 2a
= -7 - 2(5)
= -7 - 10
= -17
Tamika has a spinner with 5 equal sections – red, blue, green, yellow, and purple. She plans to spin it 150 times. Predict how many times she should expect the pointer to land on either green or yellow.
Probability helps us to know the chances of an event occurring. The number of times Tamika should expect the spinner to land on green or yellow is 60.
What is Probability?
Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Total number of sections on the spinner = 5
Number of sections with green or yellow sections = 2
Number of trials = 150
Now, the number of times Tamika should expect the spinner to land on green or yellow is,
Expected Number of lands on green or yellow = 150 × (2/5) = 60
Hence, the number of times Tamika should expect the spinner to land on green or yellow is 60.
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9. Find the value of the
underlined digit in the
following number.
739,485
Answer:
There's no underlined digit
Answer:
See below
Step-by-step explanation:
3 is in the 10 000 place = 30 000
( just put zeroes in place of all of the following numbers)
Which rules define the function graphed below? (-2,2) (0,6) (4,6)
Answer:
y = 2x + 3; y = -1/3 x + 3
Step-by-step explanation:
Both lines have y-intercept 3.
The slopes are 2 and -1/3.
The equations are: y = 2x + 3; y = -1/3 x + 3
5% dextrose infused over 8 hours. how many ml of iv fluid is infused after 6 hours?
The nurse prepares a 1,000 ml IV of 5% dextrose and water to be infused over 8 hours.
We have given that,
5% dextrose infused over 8 hours.
We have to determine the ml of iv fluid is infused after 6 hours.
What is the mixture problem?
A value mixture problem involves combining two ingredients that have different prices into a single blend.
The infusion set delivers 10 drops per milliliter.
The nurse should regulate the IV to administer approximately 21 drops per minute.
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The number of hours per week that the television is turned on is determined for each family in a sample. The mean of the data is 36 hours and the median is 32.2 hours. Twenty-four of the families in the sample turned on the television for 21 hours or less for the week. The 11th percentile of the data is 21 hours.
Step 1 of 5 : Based on the given information, determine if the following statement is true or false.
The 54th percentile is greater than or equal to 31 hours.
true or false
Using the median concept, it is found that the statement is true.
What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
In this problem, we have that the 50th percentile is of 33.2 hours, hence the 54th percentile has to be above 33.2 hours = above 31 hours, hence the statement is true.
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A Pew Research study finds that 23% of Americans use only a cell phone, and no land line, for making phone calls (The Wall Street Journal, October 14, 2010). A year later, a researcher samples 200 Americans and finds that 51 of them use only cell phones for making phone calls. Test whether the proportion of Americans who solely use cell phones to make phone calls differs from 23%. Use the .05 level of significance.
Using the z-distribution, it is found that since the p-value is greater than 0.05, the proportion does not differ from 23%.
What are the hypotheses tested?At the null hypotheses, it is tested if the proportion is of 23%, that is:
[tex]H_0: p = 0.23[/tex]
At the alternative hypotheses, it is tested if the proportion differs from 23%, hence:
[tex]H_1: p \neq 0.23[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The parameters are given as follows:
[tex]p = 0.23, n = 200, \overline{p} = \frac{51}{200} = 0.255[/tex]
The value of the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.255 - 0.23}{\sqrt{\frac{0.23(0.77)}{200}}}[/tex]
z = 0.84.
Using a calculator and considering a two-tailed test, as we are testing if the proportion is different of a value, with z = 0.84, the p-value is of 0.4.
Since the p-value is greater than 0.05, the proportion does not differ from 23%.
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Perimeter and area
What is the area of the square, circle, and shaded region?
A)
B)
C)
(a) The side length of the square is 8 m, so its area is 64 square m.
(b) The radius of the circle is 4 m, so its area is [tex](\pi)(4^{2})=16\pi[/tex] square m.
(c) Subtracting areas, we get the area of the shaded region is [tex]64-16\pi[/tex] square m.
Complete the following questions. 2 x 4² x 2 = (6 x 3²) ÷ 9 =
Answer:
4 ^x27
3
Step-by-step explanation:
2x4^2x2(6x3^2)
9
Simplifies to:
4 ^x27
3
=
4 ^x27
3
Can someone please tell me the answer to this question?
Answer:
D) 12pm
Step-by-step explanation:
8 pm = 20:00
20:00 + 16:00*4 = 20:00 + 64:00 = 84:00
subtract the 24 hours in 84:00
84:00 - 3 X 24:00 = 12:00
12:00 = 12pm
Which expression is equivalent to sin?
O sin-
sin
O sin 5
O sin 5
11
sin-
Answer: Option 4
Step-by-step explanation:
[tex]\sin \frac{7\pi}{6}=\sin \left(-\frac{\pi}{6} \right)=\sin \frac{11\pi}{6}[/tex]
Using equivalent angles, the equivalent expression to [tex]\sin{\left(\frac{7\pi}{6}\right)}[/tex] is:
[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]
What are equivalent angles?Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.
In this problem, we have that [tex]\frac{7\pi}{6}[/tex] is on the third quadrant, as [tex]\pi < \frac{7\pi}{6} < \frac{3\pi}{2}[/tex]. Hence the equivalent angle on the first quadrant is:
[tex]\frac{7\pi}{6} - \pi = \frac{7\pi}{6} - \frac{6\pi}{6} = \frac{\pi}{6}[/tex]
The sine is negative on the third and fourth quadrants, hence the equivalent angle on the fourth quadrant is:
[tex]2\pi - \frac{\pi}{6} = \frac{11\pi}{6}[/tex]
Thus, the equivalent expression is:
[tex]\sin{\left(\frac{11\pi}{6}\right)}[/tex]
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Consider the following sample of fat content of n=10 randomly selected hot dogs
The average fat content of the ten hot dog samples is: 21.91
How to calculate the average fat of hot dog samples?To calculate the average fat of the hot dog samples we must add all the values and divide the result by the number of values as shown below:
25.2 + 21.3 + 22.9 + 17.0 + 29.8 + 21.0 + 25.5 + 16.0 + 20.9 + 19.5 = 219.1219.2 ÷ 10 = 21.91Note: This question is incomplete because there is some information missing. Here is the complete information:
Question: What is the average fat of the hot dogs?
Hot Dogs' fat
Sample 1: 25.2
Sample 2: 21.3
Sample 3: 22.9
Sample 4: 17.0
Sample 5: 29.8
Sample 6: 21.0
Sample 7: 25.5
Sample 8: 16.0
Sample 9: 20.9
Sample 10: 19.5
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QUESTION IS DOWN BELOW WORTH 30 POINTS
Answer:
395.84
Step-by-step explanation:
V=πr2h=π·3^2·14
What is the area of a sector when r = 2 and 0 = 1.75 radians? [?] sq units Round your answer to the nearest tenth. Enter
Answer:
Step-by-step explanation:
The area of a sector in terms of radians as opposed to degrees is
[tex]A=\frac{\theta}{2\pi }*\pi r^2[/tex]
Filling in the formula accordingly gives us
[tex]A=\frac{1.75rad}{2\pi rad}*\pi (2)^2[/tex]
The radians cancel out, the pi's cancel out, the 2 in the denominator cancels out (divides into 2-squared once), leaving us with
A = 1.75(2) so
A = 3.5 units squared
In one lottery game, contestants pick five numbers from 1 through 23 and have to match all five for the big prize (in any order). You'll get twice your money back if you match three out of five numbers. If you buy four tickets, what's the probability of matching three out of five numbers?
(Enter your answer as a fraction in lowest terms.)
The probability of matching three out of five numbers is 153/33649
How to determine the probability?The numbers are given as:
1 to 23
There are five matching numbers
The probability of getting a match is:
p = 5-k/n where k = 0, 1, 2
While the complement probability is
q = (n - 2)/n
Using the above formulas, the probability of getting from 5 is:
P = 5/23 * 4/22 * 3/21 * 18/20 * 17/19
Evaluate the product
P = 153/33649
Hence, the probability of matching three out of five numbers is 153/33649
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Find the slope of the straight line that passes through (–2, –4) and (3, –5).
A. m= -1/5
B. m = –1
C. m = 1/5
D. m = 1
[tex]\large\boxed{\textsf{A.}\ m=-\frac{1}{5}}[/tex]
We can use the slope formula, where our points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]:
[tex]\dfrac{y_2-y_1}{x_2-x_1}[/tex]
This is also known as "rise over run" because it represents the change in vertical ([tex]y[/tex]) position divided by the change in horizontal ([tex]x[/tex]) position.
Substitute the values from the points given:
[tex]\dfrac{(-5)-(-4)}{3-(-2)}[/tex]
Subtract:
[tex]\boxed{\dfrac{-1}{5}}[/tex]
32y+54x+56=y what is y
what is the average rate of change if this function interval x = -3 to x = 0
The average rate of change of the function, over the given interval is 2.
This question is incomplete, the complete question is:
What is the average rate of change of f(x) = 2x+10, if this function interval are x = -3 to x = 0.
What is the average rate of change over the interval?The average rate of change of f(x) over the interval [a,b] is expressed as;
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Given that;
f(x) = 2x + 10Interval: [ -3, 0 ], a = -3 and b = 0We substitute our values into the expression above.
[tex]\frac{f(b)-f(a)}{b-a}\\\\\frac{f(0)-f(-3)}{0-(-3)}\\\\\frac{[2(0)+10]-[2(-3)+10]}{0-(-3)}\\\\\frac{[10]-[-6+10]}{3}\\\\\frac{[10]-[4]}{3}=\frac{6}{3}=2[/tex]
Therefore, the average rate of change of the function, over the given interval is 2.
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Find the measure of ∠2.
72°
60°
36°
54°
Answer:
(c) 36°
Step-by-step explanation:
We assume the pentagon is regular, so each central angle is congruent to the others. Each central angle is bisected by an apothem.
Angle 1Angle 1 is one of 5 congruent central angles, so its measure is ...
∠1 = 360°/5 = 72°
Angle 2Angle 2 is the result of one of the isosceles triangles having its central angle being bisected by an altitude. Its measure is half that of angle 1:
∠2 = 72°/2 = 36°
The measure of angle 2 is 36°.
Angle 3Angle 3 is the other acute angle in the right triangle in which angle 2 is one of the acute angles. Its measure is ...
∠3 = 90° -∠2 = 90° -36° = 54°
If f(x)...............
Answer:
The inverse is 5x-6
Step-by-step explanation:
To find the inverse of a function
y = ( x+6) /5
Exchange x and y
x = ( y+6)/5
Solve for y
Multiply each side by 5
5x = (y+6)/5 *5
5x = y+6
Subtract 6 from each side
5x-6 = y+6-6
5x-6 =y
The inverse is 5x-6
Step-by-step explanation:
[tex]f(x) = \frac{x + 6}{5} [/tex]
[tex] \: [/tex]
[tex]y = \frac{x + 6}{5} [/tex]
[tex] \frac{y + 6}{5} = x[/tex]
[tex]y + 6 = 5\times x[/tex]
[tex]y + 6 = 5x[/tex]
[tex]y = 5x - 6[/tex]
[tex] {f}^{ - 1} (x) = 5x - 6[/tex]
The answer is D.
Question 3
B
16 cm
38°
-C
Calculate the length of AB to 2 decimal places.
The question was incomplete. Below you can find the missing content.
ABC is a right-angled triangle.
b=16 cm
∠C=38°
Calculate the length of AB. Give your answer correct to 2 decimal places.
The picture is also attached below.
The length of the side AB is 9.85 cm.
From the triangle, it is given that
b= AC=16 cm
∠C=38°
Given that ΔABC is a right-angled triangle.
where ∠B=90°
So, here we can apply the SOH CAH TOA identity
As we know the value of sinθ is the ratio of the opposite side and the hypotenuse of the angle θ.
So, sinθ = opposite side/ hypotenuse
In triangle ΔABC
⇒ sin 38°= AB/AC
⇒ sin 38°= AB/16
⇒ AB= 16 sin 38°
⇒ AB= 9.85 cm
Therefore the length of the side AB is 9.85 cm.
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Which rule describes the composition of transformations that maps ΔDEF to ΔD''E''F''?
R0,90° ∘ T5,0(x, y)
T–5,0 ∘ R0,90°(x, y)
T5,0 ∘ R0,90°(x, y)
R0,90°(x, y) ∘ T–5,0
The transformations rule for changing DEF into D"E"F is
(b) T-5,0-RO. 90° (x,y)
Which rule describes the composition of transformations that maps ΔDEF to ΔD''E''F''?To transform a shape is to alter its dimensions and relative placement.
To convert from DEF to D"E"F, use this rule:
(b) T-5,00 RO, 90°(x, y)
From the complete question,
When DEF is spun 90 degrees counterclockwise, it becomes GH.
Then, 5 units were subtracted from the right and translated to the left.
Assume a rotation of 90 degrees counterclockwise, and write it as:
RO, 90°(x,y)
As a symbol, the leftward translation of 5 units looks like this:
T-5,0(x,y)
When both transformations are combined, we have:
T-5,0 R0.90° (x. y)
In conclusion, the transformations rule for changing DEF into D"E"F is
(b) T-5,0-RO. 90° (x,y)
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A support cable for a 56-foot tower forms a 67° angle with the ground.
What is the length of the cable to the nearest foot?
56 ft.
61 ft.
60 ft.
75 ft.
3 A bag contains red and blue marbles, such that the probability of drawing a blue marble is 8 An experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. What is the probability that both of the marbles drawn are blue? a. b. $ 24% * 39% C. d 0 14% 3 A bag contains red and blue marbles , such that the probability of drawing a blue marble is 8 An experiment consists of drawing a marble , replacing it , and drawing another marble . The two draws are independent . What is the probability that both of the marbles drawn are blue ? a . b . $ 24 % * 39 % C. d 0 14 %
Answer:
My answer: B
Step-by-step explanation:
The probability mass function of random variable X which represents the number of blue marbles drawn in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
The probability of drawing exactly one blue marble = 0.46875
Complete Question
A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. an experiment consists of drawing a marble, replacing it, and drawing another marble. The two draws are independent. A random variable assigns the number of blue marbles to each outcome.
To write the Probabilty mass function, we have to establish that in two draws with replacement, the possible number of blue marbles that can be drawn is 0, 1 and 2.
Probability of drawing a blue marble = P(B) = (3/8)
Probability of not drawing a blue marble = P(B') = 1 - (3/8) = (5/8)
- Probability of drawing 0 blue marbles in 2 draws with replacement = P(B') × P(B') = (5/8) × (5/8) = (25/64) = 0.390625
- Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
- Probability of drawing two blue marble in 2 draws with replacement = P(B) × P(B)
= (3/8) × (3/8) = (9/64) = 0.140625
The probability mass function of random variable X which represents the number of blue marbles draan in 2 draws with replacement.
X | P(X)
0 | 0.390625
1 | 0.46875
2 | 0.140625
b) Probability of drawing one blue marble in 2 draws with replacement
= [P(B) × P(B')] + [P(B') × P(B)]
= (2) × (3/8) × (5/8) = (30/64) = (15/32) = 0.46875
So, B is the answer.
What is the slope of a line parallel to the line whose equation is3x−4y=8?
−43
−34
34
43
The slope of the parallel line is 3/4
How to determine the slope?The equation is given as:
3x - 4y = 8
Rewrite as:
4y = 3x - 8
Divide through by 4
y = 3x/4 - 2
A linear equation is represented as:
y = mx + b
Where m represents the slope
By comparison:
m = 3/4
Parallel lines have equal slope
Hence, the slope of the parallel line is 3/4
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If ∠ 1 = 26 o , find the measure of ∠ 4 .
The angle ∠4 of the given transversal shown in the diagram is gotten as; 26°.
How to find alternate angles?The alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.
Now, we are told that ∠1 = 26° as seen in the attached diagram. However, it is clear that ∠2 is an alternate angle to ∠1. Thus, we can say that ∠2 = 26°.
Now, Corresponding angles are the pairs of angles that are found in the same relative position on different intersections.
From the diagram we see that ∠4 is a corresponding angle to ∠2. Thus;
∠4 = 26°.
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4. 1/37 of 111 + 1/3 of ? = 0
(1) 3
2) 9
3) 1
4) can not be determined
Answer:
4
Step-by-step explanation:
1/37 of 111+1/3 of 3= 4
1/37 of 111 +1/3 of 9=6
1/37 of 111 +1/3 of 1=3.3
In how many ways can a 7 person committee be chosen from a group of 10 people?
[tex]\displaystyle\\\binom{10}{7}=\dfrac{10!}{7!3!}=\dfrac{8\cdot9\cdot10}{2\cdot3}=4\cdot3\cdot10=120[/tex]