By the definition of complementary angles, since
∠
1
is complementary to
∠
2
,
m
∠
1
+
m
∠
2
=
90
∘
. By the vertical angles theorem,
∠
4
≃
_
∠
1
, and
m
∠
4
=
m
∠
1
by the definition of congruence. Combined with the given equation,
m
∠
4
=
40
∘
, the substitution property of equality means that
40
∘
=
m
∠
1
. Using the ,
40
∘
+
m
∠
2
=
. Finally, using the ,
m
∠
2
=
50
∘
.
Answers
Blank 1: Substitution property of equality
Blank 2: 50
Blank 3: Subtraction property of equality
The blank spaces in the task content can be filled with; Substitution property, 90° and subtraction property.
What are the missing statements in the proof?Since it follows from the vertical angles theorem that angle 1 = angle 4 as they are congruent.
Additionally, angles 1 and 2 are said to be complementary and hence, the sum of their measures is equal to 90°.
Finally, by virtue of the subtraction property of equality, the measure of angle 2 is; 90° - 40° = 50°.
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Related Questions
Find the expected value of the winnings
from a game that has the following
payout probability distribution:
Payout ($)
1 2 5 8 10
Probability 0.35 0.2 0.1 0.2 0.15
Expected Value = [? ]
Round to the nearest hundredth.
Enter
Answers
Answer:
4.35
Step-by-step explanation:
The expected value can be defined as: [tex]\sum{x_i*p_i}[/tex] where x_i = the payout, and p_i = the probability of it occurring.
This gives us the expression: [tex](1 * 0.35) + (2 * 0.2) + (5 * 0.1) + (8 * 0.2) + (10 * 0.15) = 0.35 + 0.4 + 0.5 + 1.6 + 1.5 = 4.35[/tex]
So the expected payout is 4.35
Which one of these is not a step used when constructing an inscribed square using
technology? (5 points)
1) create a circle using the center with given point tool.
2) connect the point with a line through the center of the circle.
3) mark the points of intersection between the three circles.
4) create another circle with the same radius as the original.
Answers
The correct option is option () Connect the point with a line through the center of the circle.
According to the problem,
a round planar figure whose circumference is made up of points that are equally spaced from a fixed point (the centre).referring to a unit of measurement whose area is equal to a square whose side is the specified unit.A figure that is inscribed in a circle has vertices that are points on the circle. Learn how to draw equilateral triangles, squares, and regular hexagons that are inscribed in circles, as well as how to build figures in circles.So, the correct option is option ()Connect the point with a line through the center of the circle.
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Edwin graphs the relationship of the gallons of milk he buys in terms of dollars.
Sam buys milk from a different shop. He writes an equation for the amount he spends on milk, p = 3.4g, where p is the cost and g is the gallons of milk bought. Who buys milk at a lower rate, and what is the price?
Answers
Using a proportional relationship, it is found that Sam buys milk at a lower rate, of $3.4 per gallon.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
Researching the problem on the internet, Edwin's graph goes through (2,7), hence the price is:
p = (7/2)g = 3.5g.
3.5 > 3.4, hence Sam buys milk at a lower rate, of $3.4 per gallon.
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You measure 46 textbooks' weights, and find they have a mean weight of 77 ounces. Assume the population is normally distributed with a standard deviation of 12.2 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight. Give your answers correct to at least two decimal places. Lower Limit = Upper Limit =
Answers
Using the z-distribution, the 99% confidence interval for the true population mean textbook weight is (72.37, 81.63).
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.In this problem, we have a 99% confidence level, hence[tex]\alpha = 0.99[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The other parameters are given as follows:
[tex]\overline{x} = 77, \sigma = 12.2, n = 46[/tex]
Hence the lower and upper bound of the interval are given, respectively, by:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 77 - 2.575\frac{12.2}{\sqrt{46}} = 72.37[/tex][tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 77 + 2.575\frac{12.2}{\sqrt{46}} = 81.63[/tex]More can be learned about the z-distribution at https://brainly.com/question/25890103
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The supervisor of a fish hatchery measures the length of a particular species every week after hatching to track their growth. If their average length is too short or too long, they are not maturing properly and further tests must be done to determine the cause. She randomly selects 30 fish from among those that hatched five weeks ago and measures their individual lengths in inches to determine if they have grown to an average length of 9.7 inches. She observes an average length of 10.1 inches among the sample. What set of hypotheses is she interested in testing
Answers
The z-test score is used for this hypothesis test to decide whether to reject or not to reject the null hypothesis. The z-test score for the given sample is 1.22.
How to calculate z-score for the hypothesis test?The z-score for the hypothesis test is calculated by,
z-score = (X - μ)/(σ/√n)
Where X - sample mean, μ - population mean, σ - standard deviation, and n - sample size.
Calculation:It is given that,
Sample size n = 30
Population mean μ = 9.7
Sample mean X = 10.1
Standard deviation σ = 1.8
So, the z-score is
= (10.1 - 9.7)/(1.8/√30)
= 0.4/0.328
= 1.219 ≅ 1.22
Therefore, the p-value for this z-score is 0.22. This value decides whether to reject or not to reject the null hypothesis.
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What are the answers to quick check for 13-2 equivalence with customary units of capacity in savvas
Answers
Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.
According to the question,
The customary units of capacity in Sava's are 1 fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.
Customary units and its equivalent
1 Fluid ounce = 2 Tablespoons
1 Cup = 8 fluid ounces
1 Pint = 2 cups
1 Quart = 2 pints
1 Gallon = 4 quarts
Hence, the customary units of capacity in Sava's are 1 Fluid ounce, 1 Cup, 1 Pint, 1 Quart and 1 Gallon.
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Which are the solutions of x² = -7x − 8? √17 7 √17 + 4 2 7 √17 2 4 1412 THE + 7-√17 7 + √17 2 2 O-7-√17 −7+ √17 2 4
Answers
Answer:
[tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]
Step-by-step explanation:
First, convert this into a quadratic, [tex]x^{2}+7x+8=0[/tex]. We can use the quadratic formula for this, [tex](-7[/tex]±[tex]\sqrt{7^{2}-4(1)(8)})[/tex][tex]/2(1)[/tex]. This becomes [tex](-7[/tex]±[tex]\sqrt{49-32})/2[/tex]. This is [tex](-7[/tex]±[tex]\sqrt{17}) /2[/tex]. This is your answer
In simplified form, we can write $\sqrt[3]{\sqrt[3]{54}+\sqrt[3]{250}}$ as $a\sqrt[b]{c}$, where $a$, $b$, and $c$ are all positive integers. what is $a+b+c$?
Answers
The sum of a+b+c = 307.
According to the statement
[tex]$\sqrt[3]{\sqrt[3]{54}+\sqrt[3]{250}}$[/tex] is written as [tex]$a\sqrt[b]{c}$[/tex]
now we find the sum of these
in these terms a=54 and b=3 and c=250
Then
a+b+c = 54+3+250
a+b+c = 307
So, The sum of a+b+c = 307.
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The average age of the members of a country club is 54 years old. If there are ten 36-year-olds, fifty 60-year-olds, and twenty other members all of the same age, what is the age of the twenty other members
Answers
The age of twenty other members is 48 years.
Given that the average age of the members of a country club is 54 years old and if there are ten 36-year-olds, fifty 60-year-olds, and twenty other members all of the same age.
The average is defined as the sum of a set of values divided by n, where n is the total set of values. A mean is another name for an average.
The average age is given by=(Sum of ages)/(Number of members (n))
Let x be the age of other twenty members.
Given A=54 years and n=10+50+20=80
So, now, we will substitute the values in the formula, we get
[tex]\begin{aligned}54&=\frac{10\times 36+50\times 60+20\times x}{10+50+20}\\ 54&=\frac{360+3000+20x}{80}\\ 4320&=3360+20x\end[/tex]
Further, subtract 3360 from both sides, we get
4320-3360=3360+20x-3360
960=20x
Furthermore, we will divide both sides with 20, we get
960/20=20x/20
48=x
Hence, the age of the twenty other members when average age of the members of a country club is 54 years old is 48 years.
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Can we write 0 in the form of p by q?
Answers
Answer:
Yes
=======================
Any rational number can be written in the form of p/q as per definition of a rational number.
In case with zero, it can be:
p = 0,q = any number other than zero.So, we'll have:
0/any number = 0Find the probability of winning a lottery by selecting the correct six integers, where the order in which these inte
Answers
The probability of winning a lottery by selecting the correct six integers, are
[tex]\begin{aligned}&(a) 1.68 \times 10^{-6} \\&(b) 5.13 \times 10^{-7} \\& (c) 1.91 \times 10^{-7} \\&(d)8.15 \times 10^{-8}\end{aligned}[/tex]
What is binomial distribution?The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.
Part (a); positive integers not exceeding 30.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other twenty-four.
[tex]\frac{\left(\begin{array}{c}6 \\6\end{array}\right)\left(\begin{array}{c}24 \\0\end{array}\right)}{\left(\begin{array}{c}30 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}30 \\6\end{array}\right)}=1.68 \times 10^{-6}[/tex]
Part (b); positive integers not exceeding 36.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other thirty.
[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}30 \\0\end{array}\right)}{\left(\begin{array}{c}36 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}36 \\6\end{array}\right)}=5.13 \times 10^{-7}[/tex]
Part (c); positive integers not exceeding 42.
To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the 36 other integers.
[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}36 \\0\end{array}\right)}{\left(\begin{array}{c}42 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}42 \\6\end{array}\right)}=1.91 \times 10^{-7}[/tex]
Part (d); positive integers not exceeding 48.
To calculate the probability, use binomial coefficients. Choose six of the six accurate integers and none of the other 42.
[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}42 \\0\end{array}\right)}{\left(\begin{array}{c}48 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}48 \\6\end{array}\right)}=8.15 \times 10^{-8}[/tex]
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The complete question is-
Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 30. b) 36. c) 42. d) 48.
PLEASE HELP!!!
Review the table of values for function k(x).
x
k(x)
–19.1
37.5
–19.01
37.95
–19.001
37.995
–19.0001
37.9995
–19
undefined
–18.9999
43.9995
–18.999
43.995
–18.99
43.95
–18.9
43.5
What is Limit as x approaches negative 19 plusk(x)?
37.5
38
43.5
44
Answers
The closer it gets to -19, the closer the number goes to 44. It never hits it exactly though, but based off the trend (43.95, 43.995, 43.9995) we can tell that it gets closer to 44 each time.
Hope this helps! (:
If a line that passes through the
points (8, 10) and (4, -6) also passes through the point (b, 2b), then find the value of b?
Answers
Gradient of line= (10-(-6))/(8-4)
Gradient of line= 16/4
Gradient of line= 4
Y-intercept
Y=4x+c
When x=8, y=10
10=32+c
c= -22
Equation of line
Y=4x-22
When x=b, y=2b
Y=4x-22
2b=4b-22
22=2b
b=11
Which ordered pair is a solution to the equation 2x − 3y = 1?
Answers
The ordered pair that is a solution to the equation 2x − 3y = 1 is; (2, 1)
How to find the solution that is an ordered pair?
We are given the equation;
2x - 3y = 1
Now, the ordered pair that is a solution simply means the least whole numbers for x and y that will make the equation valid.
Now, since the coefficient before x is bigger than the coefficient before y which is negative, then it means x must be larger than y. Thus, let us try x = 2 and y = 1 to get;
2(2) - 3(1) = 1
This makes the equation valid.
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You are hiking. The total weight of your backpack
and its contents is 13 3/8 pounds. You want to carry no more than
15 pounds. How many extra water bottles can you add to your
backpack if each bottle weighs 3/4 pound?
Answers
By statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .
What is the number of bottles we can add in the backpack ?It is given that the total weight of your backpack and its contents is 13 3/8 pounds.
Also given , we want to carry no more than 15 pounds.
Let the number of bottles we can carry be x.
Each bottles weigh 3/4 pounds.
Total weight of the bottles = 3x/4 pounds.
Thus, the total weight of the backpack is 13 3/8 + 3x/4 pounds .
Thus the statement equation formed is -
⇒ 107/8 + 3x/4 = 15
⇒ 3x/4 = 13/8
⇒ x = 13/6 = 2.166
∴ x ≈ 2
Therefore, by statement equation, the extra water bottles can you add to your backpack if each bottle weighs 3/4 pound is 2 .
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A plane flies 452 miles north and then 767 miles west. What is the magnitude and direction of the plane's resultant vector?
Answers
Answer:
The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north.
Step-by-step explanation:
• To find the magnitude of the resultant vector, we have to use Pythagoras's theorem:
[tex]\boxed{a^2 = b^2 + c^2}[/tex]
where:
a ⇒ hypotenuse (= resultant vector = ? mi)
b, c ⇒ the two other sides of the right-angled triangle (= 452 mil North, 767 mi West).
Using the formula:
resultant² = [tex]452^2 + 767^2[/tex]
⇒ resultant = [tex]\sqrt{452^2 + 767^2}[/tex]
⇒ resultant = 890.3 mi
• To find the direction, we can find the angle (labeled x in diagram) that the resultant makes with the north direction:
[tex]tan (x) =\frac{767}{452}[/tex]
⇒ [tex]x = tan^{-1} (\frac{767}{452} )[/tex]
⇒ [tex]x = \bf{59.5 \textdegree}[/tex]
∴ The plane's resultant vector is 890.3 miles, at an angle of 59.5° west of north .
Answer:
[tex]\displaystyle Approximately\:59°\:at\:a\:magnitude\:of\:approximately\:890\:miles[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:\theta \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:\theta \\ \frac{OPPOCITE}{ADJACENT} = tan\:\theta \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:\theta \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:\theta \\ \frac{ADJACENT}{OPPOCITE} = cot\:\theta[/tex]
We must use trigonometry to help us find the direction of the aeroplane's resultant vector. Do as I do:
[tex]\displaystyle \frac{452}{767} = cot\:x \hookrightarrow cot^{-1}\:\frac{452}{767} = x; 59,488772482...° = x \\ \\ \boxed{59° \approx x}[/tex]
Now, we will use the Pythagorean Theorem to find the magnitude of the aeroplane's resultant vector. Do as I do:
[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 767^2 + 452^2 = c^2 \\ \sqrt{792593} = \sqrt{c^2}; 890,27692321... = c \\ \\ \boxed{890 \approx c}[/tex]
Therefore, the direction and magnitude of the aeroplane's resultant vector are approximately eight hundred ninety miles at an angle of elevation of fifty-nine degrees.
I am joyous to assist you at any time.
The 40-hour work week did not become a U.S. standard until 1940. Today, many white-collar employees work more than 40 hours per week because management demands longer hours or offers large monetary incentives. A random sample of 26 white-collar employees worked on average 42.08 hours per week. Is there any evidence that the true mean number of hours worked per week by white-collar employees is greater than 40? Assume that the population standard deviation is 3.39 hours. Please use the exact value (from R) for all critical values. c) Is there any evidence to suggest the true mean number of hours worked per week by white-collar workers is greater than 40? Perform the hypothesis test at a 0.5% significance level. (0.5 pts.) Calculate the test statistic. 3.13 You are correct. Your receipt no. is 152-5185 Previous Tries (0.5 pts.) Calculate the p-value. Please write your answer in scientific notation using an E for the exponent and including at least 3 decimal places. For example, 1.234 x 10-5 would be written as 1.234E-5. 8.782x10-4 (0.5 pts.) d) Calculate the appropriate 99.5% bound that is consistent with what you did in parts b) and c).
Answers
The necessary assumptions are to get the sample for random sampling and ensure they are normal.
a. The required assumptions to form hypothesis are:Sample has to be drawn from random sampling.Sample has to be approximately normalThe samples have to be independentb. The standard deviation is known hence we have to make use of the z distribution.
c. test statistic42.08 - 40 / (3.39 /√26)
= 2.08 / 0.6648
= 3.129
≈3.13
p value
p(Z > 3.13)
= 0.0008770
8.7e-4
d. Z critical value = 2.81
42.08 +- 2.81 * 3.39/√26
= 42.08 +- 2.81*0.6648
= 42.08 - 1.868, 42.08 + 1.868
= 40.212 ,43.948
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which of the following is the product of the rational expression shown below
Answers
Answer:
B
Step-by-step explanation:
[tex]\frac{x}{x-3}[/tex] × [tex]\frac{2x}{x+5}[/tex] ( no factors cancel on numerator / denominator )
= [tex]\frac{x(2x)}{(x-3)(x+5)}[/tex]
= [tex]\frac{2x^2}{x^2+2x-15}[/tex]
Which equation represents this number sentence?
Nine more than the quotient of a number and 3 is 21.
n3+9=21
fraction n over 3 end fraction plus 9 equals 21
3n+9=21
fraction 3 over n end fraction plus 9 equals 21
n+93=21
fraction numerator n plus 9 end numerator over 3 end fraction equals 21
9n+3=21
Answers
The equation which represents the number sentence given in the task content is; n/3 + 9 = 21.
Which equation correctly represents the number sentence?According to the task content, it follows that the sentence given is; Nine more than the quotient of a number and 3 is 21.
Since, the quotient of a number and 3 can be written as; n/3.
Consequently, the correct equation is; n/3 +9 = 21.
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a 90% confidence interval for a proportion is found to be (0.22,0.28). What is the sample proportion
Answers
The value of sample proportion is found to be 0.253.
What is the sample proportion?The sample proportion [tex]\hat{p}[/tex] indicates the percentage of people in a sample who exhibit a particular quality or attribute.
Divide the number of individuals (or items) who possess the desired attribute by the overall sample size to obtain the sample proportion.
Now, according to the question;
The 90% confidence interval for a proportion is found to be (0.22,0.28).
The confidence interval for the sample is given as-
Confidence interval = Sample proportion ± Margin of Error
Let [tex]\hat{p}[/tex] be the sample proportion.
The level of significance = 1 - 0.90
= 0.10 (10%)
From z-value table, at a significance level of 5% (two-sided), z has a critical value of 1.645.
90% confidence interval = [tex]\hat{p} \pm 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Thus, 0.22 = [tex]\hat{p} - 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex], and
0.28 = [tex]\hat{p} + 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex]
Covert both equation in the form of [tex]\hat{p}[/tex] and equating to each other.
[tex]\begin{aligned}&0.22+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\&1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}+1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.28-0.22\\&2 \times 1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=0.06\\&\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\frac{0.06}{2 \times 1.645}\\&\sqrt{\frac{\hat{\nu}(1-\hat{p})}{n}}=0.02\end{aligned}[/tex]
Take square root,
[tex]\begin{gathered}\frac{\hat{p}(1-\bar{p})}{n}=0.0004 \\n=\frac{\hat{p}(1-\bar{p})}{0.0004}\end{gathered}[/tex]
Substituting the value of 'n' in the receptive equation to get the value of [tex]\begin{aligned}0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\0.22 &=\hat{p}-1.645 \times \sqrt{\frac{\hat{p}(1-\hat{p})}{p(1-\hat{p})}} \times 0.0004 \\0.22 &=\hat{p}-1.645 \times \sqrt{0.0004} \\0.22 &=\hat{p}-(1.645 \times 0.02) \\0.22 &=\hat{p}-0.033 \\\hat{p}=& 0.22+0.033=0.253\\\end{aligned}[/tex]
Therefore, the value of sample proportion is 0.253.
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A piece of PVC material weighs 0.063 pounds per cubic inch. What's the weight of a 36-inch piece of PVC pipe with an outside diameter of 0.82 inches and an inside diameter of 0.75 inches?
Answers
The weight of a 36-inch piece of PVC pipe is 0.20 pounds
How to determine the weight of a 36-inch piece of PVC pipe?The given parameters about the 36-inch piece of PVC pipe are
Height, h = 36 inches
Outside diameter, D = 0.82 inches
Inside diameter, d= 0.75 inches
The volume of the PVC pipe is then calculated as:
V = πh(D/2)^2 - πh(d/2)^2
Substitute the known parameters in the above equation
V = 3.14 * 36 * (0.82/2)^2 - 3.14 * 36 * (0.75/2)^2
Evaluate the quotients
V = 3.14 * 36 * 0.41^2 - 3.14 * 36 * 0.375^2
Evaluate the exponents
V = 3.14 * 36 * 0.1681 - 3.14 * 36 * 0.140625
Evaluate the products
V = 19.002024 - 15.89625
Evaluate the difference
V = 3.105774 cubic inches
From the question, we have:
Weight = 0.063 pounds per cubic inch
So, the total weight is
Total weight = 3.105774 cubic inches * 0.063 pounds per cubic inch
Evaluate the product
Total weight = 0.195663762 pounds
Approximate
Total weight = 0.20 pounds
Hence, the weight of a 36-inch piece of PVC pipe is 0.20 pounds
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Find the product of X^2 (4x - 3).
A. 5x^3
B. 5x^3 - 3x^3
C. 4x^3 - 3x^2
D. X^2 + 4x - 3
Answers
x² ( 4x - 3)
Apply the multiplicative law of distribution.
x² × 4x - x² × 3Multiply the monomial
4x³ - x² × 3Multiply the monomial
4x³ - 3x² ==> AnswerTherefore, the correct option is "C".
Exhibit 2 Touchdowns Field Goals Patrick 39 13 Jimmy 25 5 Exhibit 2 presents the touchdowns and field goals two football players can make if they each specialize in being either a quarterback or a kicker, but not both. Who has the absolute advantage playing quarterback
Answers
Patrick has an absolute advantage in playing quarterback.
Given a table containing touchdowns and field goals by Partrik and Field goals as under:
Person Touchdowns Field goals
Patrik 39 13
Jimmy 25 5
We are required to find a person who has an absolute advantage in playing quarterback.
Absolute advantage is the ability of an individual, company to produce greater advantage of good or service than the individual.
Total of touchdowns and field goals by Patrik=39+13=52
Total of touchdowns and field goals by Jimmy=25+5=30
We can see that total of touchdowns and field goals by Patrik is greater than total of touchdowns and field goals by Jimmy. So Patrik has an absolute advantage playing quarterback.
Hence Patrick has an absolute advantage in playing quarterback.
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Question is incomplete as it should include the following table:
Person Touchdowns Field goals
Patrik 39 13
Jimmy 25 5
The four consecutive digits $a$, $b$, $c$ and $d$ are used to form the four-digit numbers $abcd$ and $dcba$. What is the greatest common divisor of all numbers of the form $abcd dcba$
Answers
1111 is the greatest common divisor of all numbers.
Lets simplify the problem,
1234 + 4321 = 5555
2345 + 5432 = 7777
3456 + 6543 = 9999
4567 + 7654 = 12221
5678 + 8765 = 14443
6789 + 9876 = 16665
After it , we get:
5555 _=_ 101 * 11 * 5
7777 = 101 * 11 * 7
9999 = 101 * 11 * 3 * 3
12221 = 101 * 11 * 11
14443 = 101 * 11 * 13
16665 = 101 * 11 * 3 * 5
abcd(5555, 7777, 9999, 12221, 14443, 16665) = 101 * 11 = 1111
Hence we get 1111 is the greatest common divisor.
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Help me with this question please
Answers
Answer:
[tex]\dfrac{991}{40\sqrt{2}}[/tex]
Step-by-step explanation:
Given expression:
[tex]\sqrt{72}-\dfrac{48}{\sqrt{50}}-\dfrac{45}{\sqrt{128}}+2\sqrt{98}[/tex]
Rewrite 72 as 36·2, 50 as 25·2, 128 as 64·2 and 98 as 49·2:
[tex]\implies \sqrt{36 \cdot 2}-\dfrac{48}{\sqrt{25 \cdot 2}}-\dfrac{45}{\sqrt{64 \cdot 2}}+2\sqrt{49 \cdot 2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]
[tex]\implies \sqrt{36}\sqrt{2}-\dfrac{48}{\sqrt{25}\sqrt{2}}-\dfrac{45}{\sqrt{64}\sqrt{ 2}}+2\sqrt{49}\sqrt{2}[/tex]
Rewrite 36 as 6², 25 as 5², 64 as 8² and 49 as 7²:
[tex]\implies \sqrt{6^2}\sqrt{2}-\dfrac{48}{\sqrt{5^2}\sqrt{2}}-\dfrac{45}{\sqrt{8^2}\sqrt{ 2}}+2\sqrt{7^2}\sqrt{2}[/tex]
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+2\cdot 7\sqrt{2}[/tex]
Simplify:
[tex]\implies 6\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}+14\sqrt{2}[/tex]
Combine like terms:
[tex]\implies 20\sqrt{2}-\dfrac{48}{5\sqrt{2}}-\dfrac{45}{8\sqrt{ 2}}[/tex]
Make the denominators of the two fractions the same:
[tex]\implies 20\sqrt{2}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]
Rewrite 20√2 as a fraction with denominator 40√2:
[tex]\implies 20\sqrt{2}\cdot\dfrac{40\sqrt{2}}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]
[tex]\implies \dfrac{1600}{40\sqrt{2}}-\dfrac{384}{40\sqrt{2}}-\dfrac{225}{40\sqrt{ 2}}[/tex]
Combine fractions:
[tex]\implies \dfrac{991}{40\sqrt{2}}[/tex]
what is the temperature in Celsius? (LOOK AT PIC)
Answers
Answer:
21
Step-by-step explanation:
(69.8-32)×(5/9)=21
2x - y = 4
y = 2x + 4
Solution(s):
PLEASEEE
Answers
Maggie has $9 less than does her brother Ron,
who has d dollars on Tuesday. If Ron gives
Maggie $6 on Wednesday, and she does not
spend any of her money, which of the following
is an expression for the amount of money, in
dollars, that Maggie has?
A) 2d + 6
B) 2d - 3
C) d + 15
D) d-3
Answers
The expression that shows the amount of money in dollars that Maggie has d - 3
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let d represent the amount of money Ron has on Tuesday. Hence:
Money Maggie has = d - 9 + 6 = d - 3
The expression that shows the amount of money in dollars that Maggie has d - 3
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Anna and Damien are doing inventory at their pet store. Anna has counted 3 cages with 3 rabbits in each. Damien counted 4 cages with 2 rabbits in each. Which expression will help Anna and Damien count the rabbits at their store?
Answers
The expression that help Anna and Damien count the rabbits at their store is (3 * 3) + (4 * 2)
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Anna has counted 3 cages with 3 rabbits in each. Damien counted 4 cages with 2 rabbits in each. Hence:
Total rabbits = (3 * 3) + (4 * 2)
The expression that help Anna and Damien count the rabbits at their store is (3 * 3) + (4 * 2)
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PLEASE HELP GEOMETRY
answer both parts
Answers
1) vertical angles theorem
2) transitive property of congruence