a. The probability of getting exactly 451 girls in 887 births is 0.0578.
b. The probability of getting 451 or more girls in 887 births is 0.0478. To determine if 451 girls in 887 births is unusually high, we compare this probability to a significance level (alpha) of choice and then either reject or accept the null hypothesis.
c. The probability from part (b) is more relevant for trying to determine whether the technique is effective because it considers a range of outcomes that are consistent with the hypothesis that boys and girls are equally likely.
d. Based on the results, we can reject the hypothesis that boys and girls are equally likely and conclude that the gender-selection technique is effective in increasing the likelihood of having a girl.
What is probability?Probability is the likelihood of an event occurring or not occurring.
Mathematically;
Probability = expected outcomes/possible outcomea. To find the probability of getting exactly 451 girls in 887 births, we can use the binomial distribution with n = 887 and p = 0.5 (since boys and girls are equally likely).
The probability of getting k girls is given by the formula:
P(k girls) = (n choose k) * p^k * (1-p)^(n-k)
Plugging in the values, we get:
P(451 girls) = (887 choose 451) * 0.5^451 * 0.5^436
P(451 girls) = 0.0578 (rounded to four decimal places)
b. To find the probability of getting 451 or more girls in 887 births, we can add up the probabilities of getting 451, 452, 453, ..., up to 887 girls. The cumulative binomial distribution is used to determine the probability of getting k or fewer girls:
P(k or fewer girls) = sum((n choose i) * p^i * (1-p)^(n-i), i = 0 to k)
Since we want the probability of getting 451 or more girls, we can subtract the probability of getting 450 or fewer girls from 1:
P(451 or more girls) = 1 - P(450 or fewer girls)
= 1 - sum((887 choose i) * 0.5^i * 0.5^(887-i), i = 0 to 450)
= 0.0478
d. To determine if the gender-selection technique is effective, we need to compare the probability of getting 451 or more girls (from part (b)) to a significance level (alpha) of our choice.
Using an alpha set to 0.05, the probability of getting 451 or more girls in 887 births is 0.0478, it is less than 0.05. Therefore, we reject the hypothesis that boys and girls are equally likely and conclude that the gender-selection technique is effective in increasing the likelihood of having a girl.
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Combine like terms to simplify the expression:
1. 17
−
0. 07
�
+
(
−
3. 92
�
)
1. 17−0. 07a+(−3. 92a)
So the simplified expression of the expression given in the question is: 1.17 - 3.99a
To simplify the expression, we can combine the like terms, which are terms with the same variable and exponent. Starting with the first two terms: 1.17 - 0.07a. The next two terms are the opposite of each other, so we can add them: 1.17 - 0.07a + (-3.92a) = 1.17 - 0.07a - 3.92a. Finally, we can simplify the expression by combining the like terms, which are terms with the same variable: 1.17 - 0.07a - 3.92a = 1.17 - (0.07 + 3.92)a = 1.17 - 3.99a. So the simplified expression is: 1.17 - 3.99a
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Complete Question
Combine like terms to simplify the expression:
1. 17 − 0. 07 + ( − 3. 92 ) 1. 17−0. 07a+(−3. 92a)
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Determine each segment length in right triangle ABC . Right triangle ABC with right angle at vertex B. Point D lies on side AC. Dashed segment BD is drawn. Angle BAD measures 30 degrees and angle BCD measures 60 degrees. Angle BDC is a right angle. Side AC is labeled 8 and segment CD is labeled 2. 2 2 4 3 6 4 2 2 3 4 B C arrowRight A D arrowRight A B arrowRight B D
The right triangle ABC with right angle at vertex B has the length of the segment is; 4√2 unit.
What is Pythagorean theorem?The Pythagorean theorem state that in any right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two shorter sides. In this case, side AC is the hypotenuse and side AB and BC are the two shorter sides.
We can find the lengths of all three sides using the Pythagorean theorem and the information given. Side AB is equal to the square root of the sum of the squares of sides AC and BC. Since we are given that angle ABC is a right angle, we can find that side BC is equal to the length of side AB.
The side lengths are 8/2 = 4
Now, Another side length that is x
So , the equation formed is;
xcos45 = 4
x/√2 = 4
x = 4√2
Hence the length of the segment is; 4√2 unit.
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a researcher records the following data: 4, 4, 4, 4, and 3. how would you describe the variability of these data? group of answer choices it is negative because 3 is less than the other scores in the distribution. it is very small (close to 0) because scores are approximately the same. it is very large (much greater than 0) because 3 is an outlier in the data. it is equal to zero because scores are approximately the same.
The variability of the data is very small (close to 0) because all the scores are approximately the same.
The variability of these data can be calculated using the variance formula, which is the average squared difference from the mean. In this case, the mean is 3.8 (the sum of 4, 4, 4, 4, and 3 divided by 5). Therefore, the variance is 0.08 (the sum of the squared differences [4-3.8, 4-3.8, 4-3.8, 4-3.8, 3-3.8] divided by 5). This indicates that the variability of the data is very small (close to 0) because all the scores are approximately the same.
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One way of writing 75 as the sum of consecutive whole numbers is 24 + 25 + 26. How many other ways are there?
Answer:
None. [tex]24+25+26[/tex] is the only valid answer
Step-by-step explanation:
We can create an expression for the sum of 3 consecutive numbers.
[tex]S=x+(x+1)+(x+2)[/tex]
Which we can simplify to
[tex]S=x+x+1+x+2[/tex]
[tex]S=3x+3[/tex]
In this example we are given a sum of 75.
[tex]75=3x+3[/tex]
Lets solve for [tex]x[/tex].
Subtract 3 from both sides.
[tex]72=3x[/tex]
Divide both sides by 3.
[tex]24=x[/tex]
To find out what the 3 numbers are we can plug in 24 for x
[tex]x+(x+1)+(x+2)[/tex]
[tex]24+(24+1)+(24+2)[/tex]
[tex]24+25+26[/tex]
Answer:
4 other ways (5 ways, total).
Step-by-step explanation:
You want to know how many other ways 75 can be written as the sum of consecutive whole numbers other than 24+25+26.
SolutionIf 75 is written as the sum of an odd number of integers, the middle integer of the set will be 75 divided by the number of integers. The divisors of 75 are {1, 3, 5, 15, 25, 75}. If the numbers in the sum are non-negative, the number of integers involved cannot be more than √(2·75) ≈ 12. Then allowed odd numbers of integers in the sum are 3 and 5.
If 75 is written as the sum of an even number of integers, the quotient when 75 is divided by the number of integers must be 1/2 more than a whole number. Such integer divisors are 2, 6, and 10.
Sums37 + 38 = 75 . . . . 2 integers
24 + 25 + 26 = 75 . . . . 3 integers (the given sum)
13 + 14 + 15 + 16 + 17 = 75 . . . . 5 integers
10 + 11 + 12 + 13 + 14 + 15 = 75 . . . . 6 integers
3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 75 . . . . 10 integers
There are 4 other ways to use consecutive non-negative integers to make a sum of 75.
Pls help thank you will mark the Brainliest
Option d) [tex]y= 30.5(0.7)^x[/tex] is the function that best models the number of game systems sold in millions x years since 2015.
Describe Function?In mathematics, a function is a rule that associates each element in one set (called the domain) with a unique element in another set (called the range). The rule specifies how the input values (the elements of the domain) are transformed into output values (the elements of the range).
A function can be represented using various notations, such as f(x), where f is the name of the function and x is the input value, or y = f(x), where y is the output value and x is the input value. The function can be defined explicitly, as in[tex]f(x) = x^2,[/tex] or implicitly, as in the equation of a circle, [tex]x^2 + y^2 = r^2[/tex], where y is a function of x.
To determine which function best models the number of game systems sold, we need to observe the trend in the data.
We can see that the number of game systems sold is decreasing as time goes on, which means the function should be decreasing as well.
Option a) [tex]y=21.35(0.7)^x[/tex] is an exponential function with a base less than 1, which means it would also be decreasing. However, it starts with a higher initial value than the data suggests.
Option b) [tex]y= 30.5(21.35)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function does not match the trend in the data.
Option c) [tex]y= 30.5(1.3)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function also does not match the trend in the data.
Option d) [tex]y= 30.5(0.7)^x[/tex]is an exponential function with a base less than 1, which means it would be decreasing. Additionally, this function passes through all three data points, and it has a starting value that matches the first data point. Therefore, option d) is the function that best models the number of game systems sold in millions x years since 2015.
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What is the area of this compound figure?
Answer:
199 cm²
Step-by-step explanation:
in the picture
Solve for x ? Question in picture
Answer:
22
Step-by-step explanation:
x+35=56
56-35=22
x=22
how many ways can patricia choose 3 pizza toppings from a menu of 10 toppings if each topping can only be chosen once?
Step-by-step explanation:
the equation we use here is [items to choose from] to the power of [required items]; in this case, we get [tex]10^{3}[/tex].
Please need help with this math problem
Answer:
maximum value = 135
Step-by-step explanation:
the maximum value is situated at the right end of the whisker.
each division on the number line is 5 units
so maximum value = 125 + 2 units = 125 + 10 = 135
is this true or false? f (n )equals o (g (n ))space a n d space g (n )equals omega (h (n ))space t h e n space f (n )equals theta (h (n ))true false
The statement "If f(n) = O(g(n)) and g(n) = Ω(h(n)), then f(n) = Θ(h(n))" is actually true.
This can be proven using the formal definitions of the O-notation, Ω-notation, and Θ-notation:
f(n) = O(g(n)) means that there exist positive constants c and n0 such that |f(n)| ≤ c|g(n)| for all n ≥ n0.
g(n) = Ω(h(n)) means that there exist positive constants c' and n0' such that |g(n)| ≥ c'|h(n)| for all n ≥ n0'.
f(n) = Θ(h(n)) means that there exist positive constants c1, c2, and n1 such that c1|h(n)| ≤ |f(n)| ≤ c2|h(n)| for all n ≥ n1.
If we assume that f(n) = O(g(n)) and g(n) = Ω(h(n)), we can use the definitions above to show that f(n) = Θ(h(n)).
Since g(n) = Ω(h(n)), we have |g(n)| ≥ c'|h(n)| for some positive constants c' and n0', and since f(n) = O(g(n)), we have |f(n)| ≤ c|g(n)| for some positive constants c and n0.
Combining these two inequalities, we get:
|f(n)| ≤ c|g(n)| ≤ c(c'/c)|h(n)|
Therefore, f(n) = Θ(h(n)) with constants c1 = 1 and c2 = c(c'/c), and n1 = max(n0, n0').
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Please help!!
Sandra is looking to buy decorative doughnuts for a party. She is considering two local bakers. She looks up two bakers online to find how much each one charges. Here are the advertisements she saw online. Ms. Spellings Donut Shop Try out this week's special! All decorative donuts are on sale for $1.62 each with
an $8 boxing fee! Phil'd Up Doughnuts Boxing fee included in price! Number of Decorative Doughnuts and price 2 $9 4 $13 6 $17 8 $21 $25 12 $29 a) What is the rate of change and the boxing fee for each doughnut shop? b) If the total cost was Sandra's biggest concern, who should she buy from? Justify you answer mathematically.
Answer:
Step-by-step explanation:
Dont cheat on your homework
a bag of 15 scrabble tiles contains three each of the letters a, c, e, h, and n. if you pick six letters one at a time, what is the chance that you spell c-h-a-n-c-e?
A bag of 15 scrabble tiles contains three each of the letters a, c, e, h, and n. The chance of spelling "chance" is approximately 0.0108 or about 1.08%.
First, we need to count the number of ways to choose two "c"s, two "e"s, and one each of "h" and "n" from the 15 tiles in the bag. To do this, we use the combination formula:
C(n, r) = n! / (r! * (n - r)!)
where n is the total number of items and r is the number of items we want to choose. For example, to choose two "c"s from three, we can calculate:
C(3, 2) = 3! / (2! * (3 - 2)!) = 3
We can use this formula to calculate the number of ways to choose two "c"s, two "e"s, and one each of "h" and "n":
C(3, 2) * C(3, 2) * C(3, 1) * C(3, 1) = 54
Therefore, there are 54 ways to choose the required letters out of the 15 tiles in the bag.
Next, we need to count the total number of ways to choose 6 tiles from the 15 in the bag. We can again use the combination formula:
C(15, 6) = 15! / (6! * (15 - 6)!) = 5005
Therefore, there are 5005 ways to choose any 6 tiles from the bag.
Finally, we can calculate the probability of spelling "chance" by dividing the number of ways to choose the required letters by the total number of ways to choose 6 tiles:
54 / 5005 ≈ 0.0108 or about 1.08%
So the probability of spelling "chance" when picking six tiles one at a time from the bag is approximately 0.0108 or about 1.08%.
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Someone help me with this equation please!!
The given statement is transitive property.
What is transitive property?Transitive property is also called transitive property of equality when we have two equal values and either of this value is equal to third value.
DE≅XY AND [tex]\hat{DE}$$\approx\hat{XY} and \hat{XY}$$\approx$$\YZ, then\hat{DE}$$\approx$$\hat{YZ}[/tex]
This is a transitive property.
Here we have three values, initially first two values are equal and second & third values are equal.
Which gives any one of the value of first and second equals third value.
This is the transitive property.
Hence, the given statement is transitive property.
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A bathtub containing 42 gallons of water is draining at a constant rate. After 2 minutes, it holds 30 gallons of water. Write an equation that represents the number y of gallons of water in the tub after 2 minutes.
Answer:
30.
Step-by-step explanation:
We can write an equation for the number of gallons of water in the bathtub using the rate of change (drainage) and the elapsed time. Let y be the number of gallons of water in the tub after t minutes. Then, the equation can be written as:
y = 42 - (drainage rate) * t
Since we know that after 2 minutes, the tub holds 30 gallons of water, we can use this information to solve for the drainage rate:
30 = 42 - (drainage rate) * 2
12 = (drainage rate) * 2
drainage rate = 6 gallons per minute
Substituting this value into the original equation, we get:
y = 42 - 6t
So, the equation that represents the number of gallons of water in the tub after 2 minutes is:
y = 42 - 6 * 2 = 42 - 12 = 30.
Answer:
The equation representing the number of gallons of water in the tub after t minutes can be represented by a linear function y = mx + b, where y is the number of gallons of water, x is the number of minutes, m is the rate of change (or the slope) and b is the y-intercept.
Since the bathtub is draining at a constant rate, the slope (m) can be found by finding the difference between the initial number of gallons of water (42) and the number of gallons after 2 minutes (30), and dividing by the difference in time (2 minutes):
m = (42 - 30) / 2 = 6 gallons per minute
The y-intercept (b) can be found using the initial conditions of the problem, when t = 0:
b = 42 - (6 * 0) = 42
Therefore, the equation representing the number of gallons of water in the tub after t minutes can be written as:
y = 6t + 42
So, after 2 minutes, y = 6 * 2 + 42 = 54 gallons of water.
Can anyone help me with this? I’ll give brainliest and 20 points
Based on the Venn diagram, the number of people in each set are follows:
A∩B = 11 peopleThe number of people in A alone = 13The number of people in B alone = 19What is the number of people in each set in the Venn diagram?The number of people in each set in the Venn diagram is calculated as follows:
The universal set has a total of 50 people
Let the intersection of A and B be x
A∩B = x
The number of people in A alone = 24 - x
The number of people in B alone = 30 - x
x + (24 - x) + (30 - x) + 7 = 50
61 - x = 50
x = 61 - 50
x = 11
A∩B = 11
Hence;
The number of people in A alone = 24 - 11
The number of people in A alone = 13
The number of people in B alone = 30 - 11
The number of people in B alone = 19
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12. Solve the problem.
According to a college survey, 22% of all students work full time. Find the mean for the
number of students who work full time in samples of size 16.
00.2
03.5
04.0
02.8
The mean for the number of students who work full-time in
samples of size 16 are 3.5.
What is the expected value?We understand The expected value, also known as the expected average in the field of probability theory, is a generalization of the weighted average.
Given, 22% of all students work full-time, per a college poll.
Now, If we choose a sample of 16 students the mean number of students working full-time is,
= 16(22/100)
= 16×0.22
= 3.5.
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What is x and y equal to?
-10x + 4y = -14
7x + 5y = 2
Answer: x =1, y = -1
Step-by-step explanation:
-10x+4y=-14
7x+5y=2
Let's eliminate y.
5(-10x+4y= -14)
4(7x + 5y=2)
[ I multiplied the first equation by the coefficient of y in the second equation and did the same in the second equation].
=> -50x+20y =-70
28x+20y = 8
Notice how the coefficients of y are the same. We can subtract the 2 equations to eliminate y.
Thus,
-78x = -78 ( y has been eliminated)
∴ x=-78/-78 =1.
Put the value of x in any equation to find y.
7x + 5y =2
=> 7(1) + 5y =2
7+5y=2
5y = 2-7
5y = -5
y = -1.
Hope this helps :)
HELP ME PLEASE ASAP! I NEED TO PASS THIS CLASS BY MONDAY!
The length of the two sides of the given right triangle is 5√2
What is a right triangle?A triangle with an angle right angle is called a right triangle.
Given that, a right triangle, with an acute angle of 45° and the length of hypotenuse is 10 units,
We need to find the length of two sides u and v,
The sum of a triangle is 180°, and if one angle is 90° and the other is 45° therefore, the third is also 45°
Now, we know that, sides opposite to equal angles are equal,
Therefore, v = u,
Now, using the Pythagoras theorem,
10² = v²+u²
v² + v² = 100
2v² = 100
v² = 50
v = 5√2
u = 5√2
Hence, the length of the two sides of the given right triangle is 5√2
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Feb 10, 9:11:47 AM
10. Find the value of X.
The solution of x in the rhombus is 3
How to determine the solution of x in the shapeFrom the question, we have the following parameters that can be used in our computation:
The rhombus
Also, we have
LN = 14
AN = x + 4
Using the above as a guide, we have the following equation:
LN = 2 * AN
Substitute the known values in the above equation, so, we have the following representation
2 * (x + 4) = 14
Evaluate the expression
x + 4 = 7
Subtract 4 from both sides
so, we have the following representation
x = 3
Hence, the solution is 3
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Please answer with an exploration
Part A: If (26)x = 1, what is the value of x? Explain your answer. (5 points)
Part B: If (50)x = 1, what are the possible values of x? Explain your answer. (5 points)
Answer:
Part A: If (26)x = 1, the value of x is approximately 0.03846.
Part B: If (50)x = 1, the possible value of x is approximately 0.02.
Step-by-step explanation:
Part A: To find the value of x in the equation (26)x = 1, we need to find the value that, when raised to the power of 26, will equal 1. This value can be found by taking the reciprocal (or multiplicative inverse) of 26 and taking the natural logarithm of both sides.
Using the formula x = 1/26, we get:
x = 1/26 = 0.03846
So, the value of x in the equation (26)x = 1 is approximately 0.03846.
Part B: To find the possible values of x in the equation (50)x = 1, we need to find the values that, when raised to the power of 50, will equal 1. This value can be found by taking the reciprocal (or multiplicative inverse) of 50 and taking the natural logarithm of both sides.
Using the formula x = 1/50, we get:
x = 1/50 = 0.02
So, the possible value of x in the equation (50)x = 1 is approximately 0.02.
HELP will give BRAINLYST
Mrs. Harris has a piece of lumber that is 11 5/8 inches wide she plans to split the width of the lumber into three equal pieces how wide will each piece be
The size of width of each lumber piece will be 3.875 inches.
What is Algebra?Logic is the arrangement of all those concepts, whereas algebra is the study of abstract concepts.
Making something a little less complicated while both making it easier to attain or understand is the concept of clarity.
Mrs. Harris intends to divide the breadth of a piece of timber that is 11 ⁵/₈ inches broad into three equal pieces.
Convert the mixed fraction number to a decimal number. Then we have
11 ⁵/₈ = 11 + ⁵/₈
11 ⁵/₈ = 11.625 inches
The width of each lumber piece is given as,
⇒ 11.625 / 3
⇒ 3.875 inches
The size of width of each lumber piece will be 3.875 inches.
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A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 10 to 19, up to 2 above 30 to 39, up to 6 above 40 to 49, and up to 8 above 50 to 59. There is no shaded bar above 20 to 29.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 45.2 is the most accurate to use to show that they need more money.
The median of 49 is the most accurate to use, since the data is skewed.
The mean of 49 is the most accurate to use to show that they have plenty of money.
The mean of 45.2 is the most accurate to use, since the data is skewed.
The best measure of center for this data is the median, and its value is 49.
What is the median in statistics?
In statistics, the median is a measure of central tendency that represents the value separating the higher half of a dataset from the lower half.
To find the median of a dataset, the values must first be arranged in order of magnitude. If the dataset has an odd number of values, the median is the middle value. If the dataset has an even number of values, the median is the average of the two middle values.
To determine the best measure of center for this data, we need to consider the shape of the distribution. Looking at the histogram, we can see that the data is skewed to the right, with a long tail of higher values.
In this case, the median is the best measure of center, because it is not affected by the extreme values in the dataset. The median is the middle value of the dataset when it is arranged in order, and in this case, the middle value is between 49 and 50. Since there are an even number of data points, we take the average of the two middle values, which gives a median of 49.
We are given that;
The list of donation is as follows
11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59
Now,
Mean is the middle term of the data
Here,
Middle term of data = 49
Therefore, the mean of the given list will be 49.
Therefore, the best measure of center for this data is the median, and its value is 49.
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Answer: The median of 49 is the most accurate to use, since the data is skewed.
Step-by-step explanation:
in the country of united states of heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 56.6 inches, and standard deviation of 6.5 inches. a) what is the probability that a randomly chosen child has a height of less than 40.65 inches? answer
The probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.
Simply put, probability is the liability that commodity will do. When we do not know how an event will turn out, we can bandy the liability or liability of several issues. Statistics is the study of events that follow a probability distribution.
a) We need to find p(x<68.15)
Standardize x to z, we have, z = (68.15-μ)/σ
=(68.15-57)/8.1
=1.38
Reading from standard normal tables,
p(z<1.38) =0.9162.
Therefore, the probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162.
b) We need to find p(x>54.4)
Standardize x to z, we have, z = (54.4-μ)/σ
=(54.4-57)/8.1
=-0.32
Reading from standard normal tables,
p(z>-0.32) = 0.6255
Therefore, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.
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So I have to solve for x here: x/4 - 6 = x/12 + 2
Answer:
X = 48
Step-by-step explanation:
x/4 - 6 = x/12 + 2
= 3x-72=x+24
= 3x=x+96
= 2x=96
= x=48
Answer:
x=48
Step-by-step explanation:
You can solve by x by simplifying both sides of the equation, then isolating the variable
Graph the solution to the following system of inequalities.
y>-3x-5
y≥ 3x-2
Answer:
Solution to system of inequalities is y≥ 3x-2
Graph attached
Step-by-step explanation:
We have the following two inequalities:
y>-3x-5
y≥ 3x-2
To get the solution and graph
1. Graph each inequality separately
2. Choose a test point to determine which side of the line needs to be shaded
3. The solution will be the area where the shadings from each inequality overlap one another
The graph is attached. The heavily shaded region is the set of all points which satisfy all inequalities
We see that any point that satisfies y≥ 3x-2 also satisfies y>-3x-5
In other words, the solution set for y≥ 3x-2 is a subset of the solution set for y>-3x-5
SOLVING EQUATIONS Solve the equation. Check your solution.
50. y+4-1 = 18
52. v-7= 9+12
St 53.5+44=2+r
51. m+ 18+ 23 = 71
54. 22 +15=d-17
The solution of the equation are as follows:
y = 15
v = 28
r = 95.5
m = 30
d = 54
How to solve equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =. The equation can be solved by finding the value of the variables.
A variable is a number represented with letter in an equation.
Therefore, let's solve the equation.
y + 4 - 1 = 18
y = 18 - 4 + 1
y = 15
v - 7 = 9 + 12
v = 12 + 9 + 7
v = 28
53.5 + 44 = 2 + r
r = 53.5 + 44 - 2
r = 95.5
m + 18 + 23 = 71
m = 71 - 18 - 23
m = 30
22 + 15 = d - 17
d = 22 + 15 + 17
d = 54
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f(x) = -x² + 5 and g(x) = -2x+2, find all values of x for which f(x) = g(x).
Answer: Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).
Step-by-step explanation:
To find all values of x for which f(x) = g(x), we can set the two functions equal to each other and solve for x:
-x² + 5 = -2x + 2
Expanding the right-hand side:
-x² + 5 = -2x + 2
-x² + 2x + 3 = 0
Solving for x using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
where a = 1, b = 2, and c = 3
x = (-2 ± √(2² - 4(1)(3))) / 2(1)
x = (-2 ± √(4 - 12)) / 2
x = (-2 ± √(-8)) / 2
Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).
what is the number of ways to choose two toppings for a pizza, one topping from a group of 5 kinds of meats and the other topping from a group of 7 kinds of vegetables?
There are 35 ways to choose two toppings for a pizza, one topping from a group of 5 kinds of meats and the other topping from a group of 7 kinds of vegetables.
The multiplication rule of counting in Permutation and Combinations states that if there are n ways to perform one task and m ways to perform a second task, then there are n x m ways to perform both tasks in sequence.
The number of ways to choose a meat topping from 5 kinds of meats = 5.
The number of ways to choose a vegetable topping from 7 kinds of vegetables = 7.
Using the multiplication rule, the number of ways to choose one meat topping and one vegetable topping is = 5 x 7 = 35 ways.
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State how the triangles are congruent using SSS, SAS, ASA, AAS, or
HL. If they are not congruent, type NOT.
Answer:
AAS
Step-by-step explanation:
There are two pairs of congruent angles, and the pair of congruent sides is not included in between the angles.
