Answer: 0.98
Step-by-step explanation:
given data:
probability they won a game = 58% = 0.58
since outcome of games are independent, and percentage would remain same as 2014.
probablility that Dodgers wins atleast 1 of their next 7 games
= 1 - p
= 1 - ( 0.58 )^ 7
= 1 - 0.02208
= 0.98
probabikotun that Dodgers would win one of their next seven games is 0.98
Examine the two triangles. Are the triangles congruent? Justify your conclusions. If they are congruent, complete the following statement: "Yes, triangle __ congruent to triangle __ giving a detailed explanation of your reasoning. If they are not congruent, explain why you think so. Be specific in your answer and make sure to show your work.
Answer: The triangles are not congruent
==========================================
Explanation:
For triangle DEF, the missing angle D is
D+E+F = 180
D+80+60 = 180
D+140 = 180
D = 180-140
D = 40
While the missing angle K in triangle JKL is
J+K+L = 180
80+K+50 = 180
K+130 = 180
K = 180-130
K = 50
---------------------
The three angles for triangle DEF are
D = 40E = 80F = 60The three angles for triangle JKL are
J = 80K = 50L = 50We don't have all the angles matching up. We need to have the same three numbers (the order doesn't matter) show up for both triangles in order for the triangles to be congruent. This is because congruent triangles have congruent corresponding angles.
The only pair that matches is E = 80 and J = 80, but everything else is different. So there is no way the triangles are congruent.
Notice how triangle JKL has two congruent base angles (K = 50 and L = 50), so this triangle is isosceles. Triangle DEF is not isosceles as we have three different angles, so this triangle is scalene.
The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does the sample data show a significant increase in the average birthrate at a 5% level of significance?
A. Fail to reject the null hypothesis and conclude the mean is 6.6 lb.
B. Reject the null hypothesis and conclude the mean is lower than 6.6 lb.
C. Reject the null hypothesis and conclude the mean is greater than 6.6 lb.
D. Cannot calculate because the population standard deviation is unknown
Answer:
The correct option is A
Step-by-step explanation:
From the question we are told that
The population is [tex]\mu = 6.6[/tex]
The level of significance is [tex]\alpha = 5\% = 0.05[/tex]
The sample data is 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds
The Null hypothesis is [tex]H_o : \mu = 6.6[/tex]
The Alternative hypothesis is [tex]H_a : \mu > 6.6[/tex]
The critical value of the level of significance obtained from the normal distribution table is
[tex]Z_{\alpha } = Z_{0.05 } = 1.645[/tex]
Generally the sample mean is mathematically evaluated as
[tex]\=x = \frac{\sum x_i }{n}[/tex]
substituting values
[tex]\=x = \frac{9.0 + 7.3 + 6.0+ 8.8+ 6.8+ 8.4+6.6 }{7}[/tex]
[tex]\=x = 7.5571[/tex]
The standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{\frac{\sum [ x - \= x ]}{n} }[/tex]
substituting values
[tex]\sigma = \sqrt{\frac{ [ 9.0-7.5571]^2 + [7.3 -7.5571]^2 + [6.0-7.5571]^2 + [8.8- 7.5571]^2 + [6.8- 7.5571]^2 + [8.4 - 7.5571]^2+ [6.6- 7.5571]^2 }{7} }[/tex][tex]\sigma = 1.1774[/tex]
Generally the test statistic is mathematically evaluated as
[tex]t = \frac{\= x - \mu } { \frac{\sigma }{\sqrt{n} } }[/tex]
substituting values
[tex]t = \frac{7.5571 - 6.6 } { \frac{1.1774 }{\sqrt{7} } }[/tex]
[tex]t = 1.4274[/tex]
Looking at the value of t and [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis
What this implies is that there is no sufficient evidence to state that the sample data show as significant increase in the average birth rate
The conclusion is that the mean is [tex]\mu = 6.6 \ lb[/tex]
A scatter plot is shown below.. PLEASE HELPPP!!
Answer:
(0,9.8) and (10, 1.2)
Step-by-step explanation:
These are the only points that are the best fit for the garph correlation.
Answer:
(0, 9.8) and (10, 1.2)
Step-by-step explanation:
:) hope this helped
If (x - 2) and (x + 1) are factors of
x + px? + qx + 1, what is the sum of p and q?
Answer:
p + q = -3
Step-by-step explanation:
First we need to take the original equation, and factor it to a form that's easier to get two binomial factors from (i.e., let's get a quadratic):
x^3 + px^2 + qx + 1
= x (x^2 + px + q) + 1
Now that we have factored out the x, we have a quadratic trinomial which we know can be broken down into two linear binomials. The problem gives us two linear binomials, so let's take a look.
(x - 2) (x + 1) = (x^2 + px + q)
x^2 - 2x + x -2 = x^2 + px + q
Now let's solve.
x^2 - x - 2 = x^2 + px + q
-x - 2 = px + q
From here, we can easily see that p = -1 (the coefficient of x) and q = -2.
Hence, p + q = -1 + -2 = -3.
Cheers.
The following shows the monthly sales in units of six salespersons before and after a bonus plan was introduced. At 95% confidence, determine whether the bonus plan has increased sales significantly. (For the following matched samples, let the difference "d" be: d = after - before.)
Salesperson After Before
1 94 90
2 82 84
3 90 84
4 76 70
5 79 80
6 85 80
Answer:
Since the calculated value of t= 2.249 does not falls in the rejection region we therefore accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the bonus plan has not increased sales significantly.
Step-by-step explanation:
The null and alternative hypotheses as
H0: μd=0 Ha: μd≠0
Significance level is set at ∝= 0.05
n= 6
degrees of freedom = df = 6-1 = 5
The critical region is t ( base alpha by 2 with df=5) ≥ ± 2.571
The test statistic under H0 is
t = d/ sd/ √n
Which has t distribution with n-1 degrees of freedom
Sales Difference
Person After Before d = after - before d²
1 94 90 4 16
2 82 84 -2 4
3 90 84 6 36
4 76 70 6 36
5 79 80 -1 1
6 85 80 5 25
∑ 18 118
d`= ∑d/n= 18/6= 3
sd²= 1/6( 118- 18²/6) = 1/6 ( 118 - 54) = 10.67
sd= 3.266
t= 3/ 3.266/ √6
t= 2.249
Since the calculated value of t= 2.249 does not falls in the rejection region we therefore accept the null hypothesis at 5 % significance level . On the basis of this we conclude that the bonus plan has not increased sales significantly.
A positive correlation between two variables X and Y means: If the value of X is above the mean, the
value of Y will be above the mean as well.
A. This is always true.
B. This is sometimes true.
C. This is never true.
Answer: B. This is sometimes true.
Step-by-step explanation:
A positive correlation between 2 variables means that they generally move in the same direction meaning that as one variable rises, the other rises as well and as the other falls, the other falls as well.
However, the correlation can be strong, weak or anything in-between. This means that just because one variable increases by 12 does not mean the other would as well. It could increase by 1 alone and still have a positive correlation albeit a small one.
Therefore, if the value of one variable is above the mean, it doesn't always follow that the other with a positive correlation will as well as they just might not have that strong a correlation.
Factor the trinomial below. x^2 + 5x – 24 A. (x – 8)(x + 3) B. (x – 4)(x + 6) C. (x – 3)(x + 8) D. (x – 6)(x + 4)
Answer:
The answer is option CStep-by-step explanation:
x² + 5x - 24
To factorize first write 5x as a difference so that when subtracted will give you 5 and when multiplied will give you - 24
That's
x² + 8x - 3x - 24
Factorize x out
That's
x( x + 8) - 3(x + 8)
Factor x + 8 out
We have the final answer as
(x + 8)(x - 3)Hope this helps you
Answer:(x-3)(x+8)
Step-by-step explanation:
The size of the left upper chamber of the heart is one measure of cardiovascular health. When the upper left chamber is enlarged, the risk of heart problems is increased. A paper described a study in which the left atrial size was measured for a large number of children ages 5 to 15 years. Based on this data, the authors conclude that for healthy children, left atrial diameter was approximately normally distributed with a mean of 26.5 mm and a standard deviation of 4.8 mm.
Required:
a. Approximately what proportion of healthy children has left atrial diameters less than 24 mm?
b. Approximately what proportion of healthy children has left atrial diameters greater than 32 mm?
c. Approximately what proportion of healthy children has left atrial diameters between 25 and 30 mm?
d. For healthy children, what is the value for which only about 20% have a larger left atrial diameter?
Answer:
a) P [ X < 24 mm ] = 0,3015 or P [ X < 24 mm ] = 30,15 %
b) P [ X > 32 mm ] = 0,1251 or P [ X > 32 mm ] = 12,51 %
c) P [ 25 < X < 30 ] = 0,4964 or P [ 25 < X < 30 ] = 49,64 %
d) z(s) = 0,84
Step-by-step explanation:
Normal Distribution N ( μ₀ ; σ ) is N ( 26,5 ; 4,8 )
a) P [ X < 24 mm ] = ( X - μ₀ ) / σ
P [ X < 24 mm ] = (24 - 26,5)/ 4,8 = - 0,5208 ≈ - 0,52
P [ X < 24 mm ] = - 0,52
And from z-table we find area for z score
P [ X < 24 mm ] = 0,3015 or P [ X < 24 mm ] = 30,15 %
b)P [ X > 32 mm ] = 1 - P [ X < 32 mm ]
P [ X < 32 mm ] = ( 32 - 26,5 ) / 4,8
P [ X < 32 mm ] = 5,5/4,8 = 1,1458 ≈ 1,15
P [ X < 32 mm ] = 1,15
And from z-table we get
P [ X < 32 mm ] = 0,8749
Then:
P [ X > 32 mm ] = 1 - 0,8749
P [ X > 32 mm ] = 0,1251 or P [ X > 32 mm ] = 12,51 %
c) P [ 25 < X < 30 ] = P [ X < 30 ] - P [ X < 25 ]
P [ X < 30 ] = 30 - 26,5 / 4,8 = 0,73
From z-table P [ X < 30 ] = 0,7673
P [ X < 25 ] = 25 - 26,5 / 4,8 = - 0,3125 ≈ - 0,31
From z-table P [ X < 25 ] = 0,2709
Then
P [ 25 < X < 30 ] = 0,7673 - 0,2709
P [ 25 < X < 30 ] = 0,4964 or P [ 25 < X < 30 ] = 49,64 %
d) If 20 %
z- score for 20% is from z-table
z(s) = 0,84
As you wake up to get your day started, you decide to make muffins for breakfast. The recipe you are
using makes 2 dozen muffins and calls for 3 cups of flour and 1 cup of sugar. You decide to only make
18 muffins. How many cups of flour and sugar will you need for your recipe?
The above problem can easily be solved using a proportion. Show your work
Answer:
4 cups of flour is needed and 4/3 cups of sugar
Step-by-step explanation:
Given
2 dozen Muffins; 3 cups of flour and 1 cup of sugar
Required
Determine the cups of flour if 18 muffins is used
First, we have to determine the proportion of the number of muffins used previously and now;
Represent this with p;
[tex]p = \frac{2\ dozen}{18}[/tex]
[tex]p = \frac{2 * 12}{18}[/tex]
[tex]p = \frac{24}{18}[/tex]
[tex]p = \frac{4}{3}[/tex]
Multiply this to the previous cups of flours and sugars;
Cups of flour = p * previous cups of flour
[tex]Cups\ of\ flour = \frac{4}{3} * 3[/tex]
[tex]Cups\ of\ flour = 4[/tex]
Cups of Sugar = p * previous cups of sugar
[tex]Cups\ of\ sugar= \frac{4}{3} * 1[/tex]
[tex]Cups\ of\ sugar= \frac{4}{3}[/tex]
Hence, 4 cups of flour is needed and 4/3 cups of sugar
49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Group of answer choices
Answer:
Stratified Random sampling.
Step-by-step explanation:
As per the scenario, It is stratified random sampling as it divides students into strata which represent Sophomores, Juniors, and Seniors.
Simple random samples of the given sizes of the proportional to the size of the stratum which is to be taken from every stratum that is to be about 10 percent of students from every class that is selected here.
Hence, according to the given situation, the correct answer is a random stratified sampling.
A list of pulse rates is 70, 64, 80, 74,92. What is the median for this list?
Answer:
64 70 74 80 92
Answer = 74
Step-by-step explanation:
The median is when you have an order of numbers in ascending order (smallest to largest) then you find the middle number
Hope this helps :)
If anything is incorrect then please comment and I shall change the answer to the correct one
Median for the given data 70, 64, 80, 74,92 is equals to 74.
What is median?"Median is defined as the central value of the given data after arranging them into ascending or descending order."
According to the question,
Given data for pulse rates = 70, 64, 80, 74,92
Arrange the data in ascending order we get,
64, 70 , 74, 80, 92
Number of pulse rate reading is 5 , which is an odd number.
Therefore, median is the central value.
Median for the given data = 74
Hence, median for the given data 70, 64, 80, 74,92 is equals to 74.
Learn more about median here
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Average of 44.64, 43.45, 42.79, 42.28
Answer:
43.29Step-by-step explanation:
[tex]44.64+ 43.45+42.79+42.28\\\\= \frac{44.64+ 43.45+42.79+42.28}{4} \\\\\\= \frac{173.16}{4} \\\\= 43.29\\[/tex]
Techwiz electronics makes a profit of $35 for each mp3 and $18 for each DVD last week techwiz sold a combined total of 118 mp3 and DVD players. Let x be the number of mp3 sold last week write an expression for the combined total profit (in dollars) made last week
Answer:
The total profit is [tex]p = 17x + 2124[/tex]
Step-by-step explanation:
From the question we are told that
The profit made on each mp3 is k = $35
The profit made on each mp3 is y = $18
The total amount sold is n = 118
Now given that the amount of mp3 sold is x then the amount of DVD sold is mathematically evaluated as
[tex]n - x[/tex]
Now the profit made on the x number of mp3 sold is
[tex]x * 35 = 3x[/tex]
And the the profit made from the n-x number of DVD sold is 18 (n-x ) = 18 - 18x
So the total profit made last week from the sales of both mp3 and DVD is
[tex]p = 35x + 18n - 18x[/tex]
[tex]p = 17x + 18(118)[/tex]
[tex]p = 17x + 2124[/tex]
Please help!!! A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.What is the line of best fit?A.y = –0.984x + 13.5B.y = –2.9x + 13.5C.–0.984 = –2.9x + 13.5D.y = 13.5x – 2.9
Answer:
B.y = –2.9x + 13.5 i think dont word me for it
Step-by-step explanation:
Equation of line is y = –2.9x + 13.5 which is correct option(B).
What is linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
Let y = a + bx, where a is the y-intercept and b is the slope.
[tex]\sum{x} = 1 + 2 + 3 + 4 + 5 = 15[/tex]
[tex]\sum{y} = 11 + 8 + 4+ 1 + 0 = 24[/tex]
[tex]\sum {xy} = 11 + 16 + 12 + 4 + 0 = 43[/tex]
[tex]\sum{x^2} = 1 + 4 + 9 + 16 + 25 = 55[/tex]
[tex]n = 5[/tex]
[tex]b= \dfrac{n\sum{xy}-\sum{x}\sum{y}}{n{\sum{x^2}-(\sum{x}})^2}[/tex]
[tex]b= \dfrac{ 5 (43) - (15) . (24)}{{5 (55) - (15})^2}[/tex]
[tex]b= -2.9[/tex]
[tex]a = \dfrac{25}{5} - (-2.9)\dfrac{15}{5}[/tex]
[tex]a=13.5[/tex]
Hence, equation of line is y = –2.9x + 13.5
Learn more about linear equation here:
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True or false? induction is a kind of thinking you use to form general ideas and rules based on mathematical formuals
Answer:
Hey there!
True. You use individuals rules, pieces of evidence, and experimentally found ideas that can be combined to form a general mathematical statement.
Let me know if this helps :)
Jeff is playing a racing game. The game awards him an initial of virtual money. In addition, he gets of virtual money for each race he wins. In the end, he calculates average earnings of for each race he won. If represents the number of races he won, which equation can be used to find the number of wins? A. B. C. D.
Which of the following is a correct interpretation of the expression -4 - (-7)?
Answer:
D
Step-by-step explanation:
So we have the expression:
[tex]-4-(-7)[/tex]
First, simplify. Two negatives make a positive. Therefore, the -(-7) turns into +7:
[tex]-4-(-7)\\=-4+7[/tex]
When adding on the number line, we move to the right.
Therefore, the correct interpretation is the value 7 digits to the right of -4.
D is the correct answer.
Answer:
D. the number that is 7 to the right of -4 on the number line
Step-by-step explanation:
interpret -4 - (-7)
= -4 +7
therefore
the number that is 7 to the right of -4 on the number line
so its D.
Brainliest for the correct answer!! A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table.What is the line of best fit?A.y = –0.984x + 13.5B.y = –2.9x + 13.5C.–0.984 = –2.9x + 13.5D.y = 13.5x – 2.9
Answer:
B. y = –2.9x + 13.5
Step-by-step explanation:
You can try to use the calculator to determine the best line for the values given; you will se that the calculator form, for the linear function is
y = a + bx, where a is the y intercept and b is the slope.
To determine the slope, we apply a formula, to calculate the product of the two xy and, x², plus the sum of each column.
x y xy x²
1 . 11 = 11 → x² = 1² = 1
2 . 8 = 16 → x² = 2² = 4
3 . 4 = 12 → x² = 3² = 9
4 . 1 = 4 → x² = 4² = 16
5 . 0 = 0 → x² = 5² = 25
Total x = 1 + 2 + 3 + 4 + 5 = 15
Total y = 11 + 8 + 4+ 1 + 0 = 24
Sum of xy = 11 + 16 + 12 + 4 + 0 = 43
Sum of x² = 1 + 4 + 9 + 16 + 25 = 55
n = 5
So b = 5 (43) - (15) . (24) / 5 (55) - 15² = -2.9
a = y media - b . x media → a = 24/5 - (-2.9) . 15/5 = 13.5
Assume that when adults with smartphones are randomly selected, 57% use them in meetings or classes. If 8 adult smartphone users are randomly selected, find the probability that exactly 4 of them use their smartphones in meetings or classes. The probability is
Answer:
≈ 0.2526
Step-by-step explanation:
The number of combinations of 4 out of 8:
8C4 = 8!/(4!(8-4)!)= 8*7*6*5/(1*2*3*4)= 70Success factor is:
57% = 0.57and failure factor is:
(100 - 57)%= 43%= 0.43Probability:
0.57⁴*0.43⁴*70 ≈ 0.2526The mean number of rushing yards for one NFL team was less than 99 yards per game. If a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?
Question options :
A. There is sufficient evidence to reject the claim
u < 99.
B. There is sufficient evidence to support the claim
u < 99.
C. There is not sufficient evidence to reject the claim
u < 99.
D. There is not sufficient evidence to support the claim
u< 99.
Answer:
B. There is sufficient evidence to support the claim
u < 99.
Step-by-step explanation:
We construct the n*ll and alternative hypotheses to support our claim
The n*ll hypothesis :H0
The alternative hypothesis : Ha
N*ll hypothesis =H0: u=99
Alternative hypothesis =Ha: u<99
So if n*ll hypothesis (H0) u=99 is rejected, then we accept the alternative hypothesis that u<99
we can therefore have sufficient evidence to support our claim that u<99
A number is chosen at random from the set of consecutive natural numbers $\{1, 2, 3, \ldots, 24\}$. What is the probability that the number chosen is a factor of $4!$? Express your answer as a common fraction.
Answer:
[tex]Probability = \frac{1}{3}[/tex]
Step-by-step explanation:
Given
[tex]Set:\ \{1, 2, 3, \ldots, 24\}[/tex]
[tex]n(Set) = 24[/tex]
Required
Determine the probability of selecting a factor of 4!
First, we have to calculate 4!
[tex]4! = 4 * 3 * 2 * 1[/tex]
[tex]4! = 24[/tex]
Then, we list set of all factors of 24
[tex]Factors:\ \{1, 2, 3, 4, 6, 8, 12, 24\}[/tex]
[tex]n(Factors) = 8[/tex]
The probability of selecting a factor if 24 is calculated as:
[tex]Probability = \frac{n(Factor)}{n(Set)}[/tex]
Substitute values for n(Set) and n(Factors)
[tex]Probability = \frac{8}{24}[/tex]
Simplify to lowest term
[tex]Probability = \frac{1}{3}[/tex]
Help please, I’m confused about this question.
Answer:
The order, least to greatest, is:
Lemon, Cherry, Grape.
Step-by-step explanation:
Adding all these values up, we get to 1. This means that the smallest values will be the least likely and the highest values will be the most likely.
With the numbers 0.2, 0.16, and 0.64, we can sort these by value.
0.16 is the smallest.
0.2 is the next biggest
and 0.64 is the largest number.
So, the order is Lemon, Cherry, Grape.
Hope this helped!
Plz answer quickkkk help will give 5 star rate if answer is right nd will say thx
Answer:
To find the x-intercept, substitute in 0 for y and solve for x.
To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s):
(−6,0)
y-intercept(s):
(0,3)
So I would say -6 and 0 and 2 are in domain
Answer:
-6, 0 ,2 are in the domain
Step-by-step explanation:
The domain is what values that x can take
There are no restrictions on the values that x can take
All real numbers are in the domain
-6, 0 ,2 are in the domain
m= -1/2 and the point (3, -6) which is the point -slope form of the equation
Answer:
y+6=-1/2(x-3)
Step-by-step explanation:
Point slope form: y-y1=m(x-x1)
Given that:
m=-1/2 and point (3, -6), you just add these numbers into the equation, and this gives:
y+6=-1/2(x-3)
Hope this helped!
Have a nice day!
The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places. 800 grams = ______ pounds 700 grams = _____ pounds
Answer:
800= about 1.76 lbs
700= about 1.54 lbs
(there are about 453.5 grams in a pound
Step-by-step explanation:
Answer:
800 grams = 1.76 pounds
700 grams = 1.54 pounds
Step-by-step explanation:
i googled it
A low-noise transistor for use in computing products is being developed. It is claimed that the mean noise level will be below the 2.5-dB level of products currently in use. It is believed that the noise level is approximately normal with a standard deviation of .8. find 95% CI
Answer:
The 95% CI is [tex]2.108 < \mu < 2.892[/tex]
Step-by-step explanation:
From the question we are told that
The population mean [tex]\mu = 2.5[/tex]
The standard deviation is [tex]\sigma = 0.8[/tex]
Given that the confidence level is 95% then the level of confidence is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
=> [tex]\alpha = 5\%[/tex]
=> [tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the values is [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
here we would assume that the sample size is n = 16 since the person that posted the question did not include the sample size
So
[tex]E = 1.96* \frac{0.8}{\sqrt{16} }[/tex]
[tex]E = 0.392[/tex]
The 95% CI is mathematically represented as
[tex]\= x -E < \mu < \= x +E[/tex]
substituting values
[tex]2.5 - 0.392 < \mu < 2.5 + 0.392[/tex]
substituting values
[tex]2.108 < \mu < 2.892[/tex]
Please help 1-7 questions
Answer:
25= q+20
25 - 20 =q
5 = q
Hi there! Hopefully this helps!
-------------------------------------------------------------------------------------------
Answer: q = 5.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[tex]25 = q + 20[/tex]
Swap sides so that all variable terms are on the left hand side.
[tex]q + 20 = 25[/tex]
Subtract 20 from both sides.
[tex]q = 25 - 20[/tex]
Subtract 20 from 25 to get, you guessed it, 5!1/9, -0.1, -2/12 in order
Answer:
-2/12, -0.1, 1/9
Step-by-step explanation:
Answer:
Least to greatest: -2/12 , -0.1 , 1/9
Greatest to least: 1/9, -0.1, -2/12
Step-by-step explanation:
Change all of the numbers so that they are either fractions or decimals. Usually it is easier to change all the numbers to decimal.
Divide:
1/9 = ~0.111 (rounded)
-0.1 = -0.1
-2/12 = - ~0.167 (rounded)
Put the numbers in number order:
-~0.167 , -0.1 , ~0.111
-2/12 , -0.1 , 1/9
~
The size of a television is the length of the diagonal of its screen in inches. The aspect ratio of the screens of older televisions is 4:3, while the aspect ratio of newer wide-screen televisions is 16:9. Find the width and height of an older 35-inch television whose screen has an aspect ratio of 4:3.
Answer:
The Width = 28 inches
The Height = 21 inches
Step-by-step explanation:
We are told in the question that:
The width and height of an older 35-inch television whose screen has an aspect ratio of 4:3
Using Pythagoras Theorem
Width² + Height² = Diagonal²
Since we known that the size of a television is the length of the diagonal of its screen in inches.
Hence, for this new TV
Width² + Height² = 35²
We are given ratio: 4:3 as aspect ratio
Width = 4x
Height = 3x
(4x)² +(3x)² = 35²
= 16x² + 9x² = 35²
25x² = 1225
x² = 1225/25
x² = 49
x = √49
x = 7
Hence, for the 35 inch tv set
The Width = 4x
= 4 × 7
= 28 inches.
The Height = 3x
= 3 × 7
= 21 inches
A museum curator is hanging 7 paintings in a row for an exhibit. There are 4 Renaissance paintings and 3 Baroque paintings. From left to right, all of the Renaissance paintings will be hung first, followed by all of the Baroque paintings. How many ways are there to hang the paintings
Answer:
144 ways
Step-by-step explanation:
Number of paintings = 7
Renaissance = 4
Baroque = 3
We are hanging from left to right and we will first hang Renaissance painting before baroque painting.
For Renaissance we have 4! Ways of doing so. 4 x3x2x1 = 24
For baroque we have 3! Ways of doing so. 3x2x1 = 6
We have 4!ways x 3!ways
= (4x3x2x1) * (3x2x1) ways
= 144 ways
Therefore we have 144 ways to hang the painting.
