Answer:
The perimeter is approximately 6.40.
Step-by-step explanation:
To find the perimeter of a triangle with vertices X (1, 3), Y (-4, -1), and Z (4, -1), we can first find the distance between each pair of points using the distance formula.The distance between points X and Y is:
$d(X,Y) = \sqrt{((1 - (-4))^2 + (3 - (-1))^2)} = \sqrt{25 + 16} = \sqrt{41}$
The distance between points Y and Z is:$d(Y,Z) =
\sqrt{((-4 - 4)^2 + ((-1) - (-1))^2)} = \sqrt{0 + 0} = 0$
The distance between points X and Z is:
$d(X,Z) = \sqrt{((1 - 4)^2 + (3 - (-1))^2)} = \sqrt{9 + 16} = \sqrt{25}$
We can then find the perimeter of the triangle by adding up the lengths of the sides. In this case, the perimeter is $d(X,Y) + d(Y,Z) + d(X,Z) = \sqrt{41} + 0 + \sqrt{25} = \sqrt{41} + \sqrt{25} = 6.40\ldots$.
Rounded to two decimal places, the perimeter is approximately 6.40.
The Tri-State Pick 3 lottery game offers a choice of several bets. You choose
a three-digit number. The lottery commission announces the winning three-digit number,
chosen at random, at the end of each day. The "box" pays $83.33 if the number you choose
has the same digits as the winning number, in any order. Find the expected payoff for a
$1 bet on the box. (Assume that you chose a number having three different digits.)
Answer: The Tri-State Pick 3 lottery game offers a choice of several bets, including a "box" bet where you choose a three-digit number and win if the number you choose has the same digits as the winning number, in any order. The expected payoff for a $1 bet on the box is $83.33.
To find this expected value, we need to consider all the possible ways that the winning number could be chosen and calculate the probability of each outcome. Since the winning number is chosen at random, each of the 10 possible digits (0 through 9) is equally likely to be chosen for each of the three positions in the winning number.
Since the box bet pays off if the digits of your chosen number match the digits of the winning number, regardless of their order, the number of winning combinations is equal to the number of ways to arrange the three digits of the winning number. This is equal to 3! (3 factorial), which is equal to 6.
Since there are a total of 10 possible digits for each position and the winning number has three positions, there are a total of 10 x 10 x 10 = 1000 possible winning numbers. Of these, 6 will pay off for a box bet, so the probability of winning a box bet is 6/1000 = 0.006.
Since the expected value of a bet is equal to the probability of winning multiplied by the payoff, the expected value of a $1 bet on the box is 0.006 x $83.33 = $0.05. Therefore, the expected payoff for a $1 bet on the box is $0.05.
The school's math team has 14 new members this year, which makes a total of 34. The number of new members represents about what percent of the total membership?
41% of the math team's total members are brand-new recruits.
What is percentage ?It is the ratio of two integers expressed as a decimal fraction of a whole number. It is a statistic for contrasting two sets of data, and the % sign is used to describe it as a percentage.
Percentages are often and creatively used. For instance, a lot of data is published as percentages in the media, including bank interest rates, retail discounts, and inflation rates. Percentages are essential for grasping the financial aspects of daily living.
The percentage of the entire membership that the number of new members represents is determined to be
=(14/34)×100
=41 %
0.41 x 100 = 41%
This means that 41% of the club is new members!
Thus, the number of new members is 41% of the total membership of the maths team.
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A fast food outlet claims the mean waiting time in line is less than 3. 5 minutes. A random sample of 20 customers has a mean of 3. 7 minutes with a standard deviation of 1 minute. What will be the test statistic?.
Answer:
To determine the test statistic for this problem, we need to first calculate the standard error of the mean. This is given by the formula:
Standard error of the mean = Standard deviation / sqrt(n)
where n is the number of samples in the population. In this case, the standard deviation is 1 minute and the number of samples is 20, so the standard error of the mean is equal to 1 / sqrt(20) = 0.22.
We can now use this value to calculate the test statistic, which is given by the formula:
Test statistic = (Sample mean - Population mean) / Standard error of the mean
In this case, the sample mean is 3.7 minutes, the population mean is less than 3.5 minutes, and the standard error of the mean is 0.22. Since the population mean is less than 3.5 minutes, we will use 3.5 as the value for the population mean in our calculation. Plugging these values into the formula, we get:
Test statistic = (3.7 - 3.5) / 0.22 = 0.22 / 0.22 = 1
Therefore, the test statistic for this problem is 1. This value indicates that the sample mean is slightly higher than the population mean, but not by a significant amount.
∠Cis a right angle and AB=14 miles, determine the length of BC and AC.
The length of BC is approximately 5.72 miles and the length of AC is approximately 12.67 miles.
Let's represent the length of the side opposite angle A "BC" and the length of the side adjacent to angle A "AC". We can then use the sine function to find BC:
sin(A) = BC / AC
Substituting the given values, we get:
sin(24°) = BC / 14
We can use a calculator or look up the value of sin(24°) to get:
sin(24°) ≈ 0.406
Solving for BC, we get:
BC = 14 * sin(24°) ≈ 5.72
To find AC, we can use the cosine function:
cos(A) = AC / AC
Substituting the given values, we get:
cos(24°) = AC / 14
We can use a calculator or look up the value of cos(24°) to get:
cos(24°) ≈ 0.913
Solving for AC, we get:
AC = 14 x cos(24°) ≈ 12.67
Thus, BC is about 5.72 miles long while AC is about 12.67 miles in length.
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The equation 4(2x 1) = 6x − 12 models the change in water level in a lake in one month. solve for x, which is change in height in inches. x equals negative thirteen halves x = −8 x = 8 x equals eleven halves
From the given options, option 2. x= -8 is the correct option. Here, the x is change in height in inches so the, change in height is -8 inches.
A linear equation is simply an equation with the highest degree always being 1. The standard form of a linear equation in one variable is Ax + B = 0. x is a variable in this equation, and A and B are constants. A two-variable linear equation has the standard form Ax + By = C. The variables x and y are variables, their coefficients A and B are variables, and C is a constant.
Given, linear equation is
[tex]4(2x+1)=6x-12\\\\8x+4=6x-12\\\\8x-6x=-4-12\\\\2x=-16\\\\x=-8[/tex]
Hence, the x equals to -8.
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What is the smallest prime number that is the sum of two other distinct prime numbers?
Answer:
5
Step-by-step explanation:
2 +3 = 5
Need help with this equation and graphing table asap!! Look at the image
first 2;
a) 7(2) + 8 = 22 > 16, 7(4) + 8 = 36>32
36 - 22 = 14/2 = 7
32 - 16 = 16/2 = 8
7<8
the table has a greater rate of change
y intercept
equation; 8
table; 0
8> 0
the equation has a greater y intercept
Find the number of degrees for the sum of the interior angles of a regular 12-sided figure.
Answer:
Sum of 12-sided polygon=1800°
Measure of each interior angle of a regular12-sided polygon=150°
Help!!!! Please Help Me!!! I need the answer right now!!! Thanks!!!
The subject is Science and Not Mathematics.
I couldn't find the Science option.
The numbers of the atoms of each element are;
Carbon dioxide;6 atoms of carbon, 12 atoms of oxygen
Water ;12 atoms of hydrogen, 6 atoms of oxygen
Glucose;6 atoms of carbon, 12 atoms of hydrogen, 6 atoms of oxygen
Oxygen molecule12 atoms of oxygen
What is a reaction?In a chemical reaction, there is the combination of the atoms of the reactants and a consequent recombination as the products are formed. In accordance with the law of the conservation of mass, we know that the number of atoms before reaction must be equal to the number of atoms after reaction.
Now we have to look at the atoms and count up the number of atoms of each element in each of the compounds and this is how we are able to obtain the number of each atom as shown above.
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n- ? 1) When loan officers speak to people about taking out a loan for a certain principal, P at a certain monthly rate, they always have to balance two quantities, the monthly payment, m] with the number of payments, n] it takes to pay off the loan. These two vary inversely. All of these quantities can be related by the formula: Por 1-(1+r)¯" m= Calculate the monthly payment needed to pay off a $200,000 loan at 4% yearly interest over a 20-year period.. 110
[tex]m = \frac{200000.1/3}{1-(2/3)^{-240} }[/tex] is the monthly payment
What is Compound interest?
Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
According to given question:
Principle Amount (P) = $200, 000
Rate(r) = 4% yearly
Rate(r) = 4/12 % Monthly
Rate(r) = 1/3 % Monthly
Time = 20 years = 240 months
⇒ 240 is the number of payment needed to pay
n = 240
Therefore, the monthly payment needed to pay
⇒ [tex]m = \frac{P.r}{1-(1-r)^{-n} }[/tex]
⇒ [tex]m = \frac{200000.1/3}{1-(1-1/3)^{-240} }[/tex]
⇒ [tex]m = \frac{200000.1/3}{1-(2/3)^{-240} }[/tex]
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1. Which of the following is a perfect cube. (A) 100 (B) 68600 (C) 343000 (D) 400
Answer: 68600
hope it helps!
Cora plans to buy some calligraphy pens priced at $5 each. Write an equation that shows how the total cost, y, depends on the number of calligraphy pens Cora buys, x. Do not include dollar signs in the equation.
Answer: y = 5x
Step-by-step explanation:
Percents, decimals, and fractions
Answer:
1.) 0.25
2.) 0.50
3.) 0.125
4.) 2.25
Step-by-step explanation:
When turning percentages into decimals, you move the decimal point two places to the left.
EX:
25%
25.0 (move the decimal point two places to the left)
2.5
.25
0.25 (add any zeros if necessary)
Hope this helps!!
Tip:It doesn't matter where the decimal point is in a percentage, as long as you move the point two places to the left, you are still turning it into a decimal.
Julie buys a pair of earrings for $7. Now she would like to buy the same earrings for 2 of her friends. How much will she spend for all 3 pairs of earrings
On Thursday the Meat King Market sold 210 pounds of ground beef. On Friday they sold twice
that amount. On Saturday they only sold 130 pounds. How much more meat did they sell on
Friday than Saturday?
Answer:
290
Step-by-step explanation:
210 x 2 = 420
420 - 130 = 290
set the two equations to each other then solve for x y=2x-3
Answer:
The value of x is (y + 3)/2
Step-by-step explanation:
y = 2x - 3
y + 3 = 2x - 3 + 3
y + 3 = 2x
2x/2 = (y + 3)/2
x = (y + 3)/2
Thus, The value of x is (y + 3)/2
Answer:
x = (y + 3)/2
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ y = 2x - 3
Then the value of x will be,
→ y = 2x - 3
→ 2x - 3 = y
→ 2x = y + 3
→ x = (y + 3)/2
→ x = (y/2) + (3/2)
Hence, answer is x = (y + 3)/2.
Jill made a popcorn container that is shaped like a cone. The diameter of the opening is 8 inches and the height is 9 inches. What is the volume of the popcorn container? Leave answer alone, do not round.
Help with question 4
Answer:
It is 11-9/16
Step-by-step explanation:
1.
The band and the orchestra are each having a party to celebrate the
results of their latest competition. The band would like to order cupcakes
from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee
The orchestra would like to order cupcakes from Publix at $2.90 each
and a $22.50 order fee. This system {2.90c +22.50 represents the
total cost, T, and the number of cupcakes. Determine how many
cupcakes each club can order if they both have the same amount of
money to spend. Is the solution viable or not viable?
By solving a linear equation, it can be calculated that
Each club can order 21.1 cupcakes if they both have the same amount of
money to spend
What is a linear equation?
Equation shows the comparison between two algebraic expressions by connecting the two algebraic expressions by an equal to sign
A one degree equation is called linear equation
Let the number of cupcakes ordered by each club be c
The band would like to order cupcakes from Walmart at a cost of $3.35 per cupcake and a $13.00 order fee
Total amount spent = $(13 + 3.35c)
The orchestra would like to order cupcakes from Publix at $2.90 each
and a $22.50 order fee
Total amount spent = $(22.5 + 2.90c)
By the problem,
The linear equation is
13 + 3.35c = 22.5 + 2.90c
3.35c - 2.90c = 22.5 - 13
0.45c = 9.5
c = 21.1
This solution is not viable as the number of cupcakes must be an integer not a decimal.
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juan is trying to save pizza from dinner, so he can bring pizza to school for lunch he bought 1 3/7 od pepperoni pizza and ate 1 1/3 of the pepperoni pizza how much pizza does he have left to bring to school?
Answer:
i think 2/21 i think im wrong
Step-by-step explanation:
Pleaseeee help I’m so confused
Answer:
D
Step-by-step explanation:
if you move the preimage on the image you can see that the two figures are equals
how would increases in tolerable misstatement and assessed level of control risk affect the sample size in a substantive test of details
Increases in tolerable misstatement will decrease sample size and assessed level of control risk will Increase sample size in a substantive test of details.
Sample size will be decreased when there is an increase in tolerant misstatement because there is a deviation that does not impact the financial statement. An increase in the assessed level of control risk, on the other hand, will increase sample size because the risk of material misstatements has also increased.
Complete question:-
How would increases in tolerable misstatement and assessed level of control risk affect the sample size in a substantive test of details?
a. Increase in Tolerable Misstatement = Decrease sample size. Increase in Assessed Level of Control Risk = Decrease sample size
b. Increase in Tolerable Misstatement = Decrease sample size. Increase in Assessed Level of Control Risk = Increase sample size
c. Increase in Tolerable Misstatement = Increase sample size. Increase in Assessed Level of Control Risk = Decrease sample size
d. Increase in Tolerable Misstatement = Increase sample size. Increase in Assessed Level of Control Risk = Increase sample size
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1. $3.96 x 5
2. 0.023 x 40
3. 0.67 x 61
4. $19.99 x 6
5. 0.13 x 57
6. 0.041 x 15
Answer:
1. $19.80
2. 0.92
3. 40.87
4. 119.94
5. 7.41
6. 0.615
Step-by-step explanation:
1. $3.96 x 5 = $19.80
2. 0.023 x 40
⇒ 0.023 x 10 = 0.23
⇒ 0.23 x 4 = 0.92
3. 0.67 x 61
⇒ 0.67 x 1 = 0.67
⇒ 0.67 x 60 = 40.2
⇒ 0.67 + 40.2 = 40.87
4. $19.99 x 6
⇒ 19.99 x 6 = 119.94
5. 0.13 x 57
⇒ 0.13 x 50 = 6.5
⇒ 0.13 x 7 = 0.91
⇒ 6.5 + 0.91 = 7.41
6. 0.041 x 15
⇒ 0.041 x 10 = 0.41
⇒ 0.041 x 5 = 0.205
⇒ 0.41 + 0.205 = 0.615
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Fátima, Gabriel y José tienen un total de $1080 en sus carteras. Gabriel tiene 3 veces lo que José tiene. Fátima tiene $70 menos
que José. ¿Cuanto dinero tienen en sus carteras?
Fátima tiene un total de $ 160, Gabriel tiene un total de $ 690 y José tiene un total de $ 230.
¿Cómo determinar el dinero requerido en sus carteras?
En este problema tenemos a tres personas, Fátima, Gabriel y José, que reúnen un total de $ 1.080. A continuación, traducimos las variables y ecuaciones asociadas a la situación:
x - Cantidad de dinero de Fátima.
y - Cantidad de dinero de Gabriel.
z - Cantidad de dinero de José.
Ecuaciones: Fátima, Gabriel y José tienen un total de $ 1080.
x + y + z = 1080
Gabriel tiene 3 veces lo que José tiene.
y = 3 · z
Fátima tiene $ 70 menos que José.
x = z - 70
A continuación, resolvemos el sistema de ecuaciones lineales:
x + y + z = 1080
(z - 70) + 3 · z + z = 1080
5 · z - 70 = 1080
5 · z = 1150
z = 1150 / 5
z = 230
x = z - 70
x = 230 - 70
x = 160
y = 3 · z
y = 3 · 230
y = 690
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The ratio of females to males at a movie is 8 7 If there are 28 males how many females
are in the movie
Answer: 32 females
Step-by-step explanation:
28 divided by 7 = 4
so, multiply 8 by 4 as well.
Answer: 32 females are at the movie
Step-by-step explanation:
8(females):7(males)
x:28
28/7= 4
x=4x8
x=32
There are 32 females
Aniyah invests $2300 in one account and $1400 in an account paying 4 % higher interest. At the end of one year she had earned $130 in interest. At what rates did she invest
The rate of interest in one account whose investment is $2300 will be 3.21%.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Aniyah puts $2300 in one record and $1400 in a record paying 4 % higher interest. Toward the finish of one year, she had procured $130 in interest.
Let 'x' be the interest. Then the equation is given as,
(2300 × x × 1)/100 + (1400 × 4 × 1) / 100 = 130
Simplify the equation, then we have
23x + 56 = 130
23x = 74
x = 3.21%
The pace of revenue in one record whose speculation is $2300 will be 3.21%.
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in a hypothetical case-control study of female participants regarding exposure to emf's and breast cancer, the following data were obtained: 11 cases exposed, 108 controls exposed, 5 cases not exposed, 436 controls not exposed. what is the odds ratio for the association between exposure to emf's and breast cancer?
The odds ratio for the association between exposure to emf's and breast cancer would be (11/5) / (108/436) = 2.2.
1. Calculate the odds of exposure for cases: 11/5 = 2.2
2. Calculate the odds of exposure for controls: 108/436 = 0.25
3. Divide the odds of exposure for cases by the odds of exposure for controls: 2.2/0.25 = 8.8
4. Finally, the odds ratio for the association between exposure to EMF's and breast cancer is 2.2.
The odds ratio for the association between exposure to EMF's and breast cancer can be calculated by dividing the odds of exposure for cases by the odds of exposure for controls. To calculate this, first take the number of cases exposed (11) and divide it by the number of cases not exposed (5). This will give the odds of exposure for cases (2.2). Second, take the number of controls exposed (108) and divide it by the number of controls not exposed (436). This will give the odds of exposure for controls (0.25). Finally, divide the odds of exposure for cases (2.2) by the odds of exposure for controls (0.25). This will give the odds ratio for the association between exposure to EMF's and breast cancer (2.2).
Odds ratio = (11/5) / (108/436) = 2.2
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Is this true or false?
TRUE: The given contrapositive statement are correct,
If m ≤ 3, then, m < 5.
Explain the contrapositive statement?An inference rule called proof by contrapositive, also known as proof by contraposition, is used in proofs to infer a conditional assertion from its contrapositive. To put it another way, the assertion "if B, then not A" is proven rather than the conclusion "if A, then B."When you reverse the hypothesis as well as the conclusion in a statement and reject both of them, you have a contrapositive statement.For the stated conditional statement -
If m ≤ 3, then, m < 5.
Then, contrapositive statement for the given statement will be
(m < 5)' ⇒ (m ≤ 3)'
That is;
(m > 5) ⇒ (m > 3)
That is, if m> 5 then, m > 3, which is true.
Thus, the contrapositive statement for the given conditional statement is true.
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9. A straight line passes through points (2, 12) and (3, 8). What is the equation of the
line?
Which of the following choices is not an example of a unit rate?
earnings per hour dollars per pound calories per serving $25.50 for 5 gallons
Examples of unit rates are Dollars per pound calories and earnings per hour. The rest is not the unit rate.
What is the unit rate?
An item's unit rate is its price for one of them. This is expressed as a ratio with a one as the denominator. For instance, if you covered 70 yards in 10 seconds, you covered 7 yards on average every second. 70 yards in 10 seconds and 7 yards in 1 second are both ratios, although only the latter is a unit rate.
Earnings per hour are a unit rate since it is calculated for an hour.
Dollars per pound calories is a unit rate.
Serving $25.50 for 5 gallons is not a unit rate, the cost is for 5 gallons. If the cost is for 1 gallon then it will unit rate.
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