Length of side |FD| is approximately 3.2
The measure of angle F, m ∠F, is approximately 59.6°
The measure of angle E, m ∠E, is approximately 30.4°
Calculating the length of sides and measure of angles in a triangleFrom the question, we are to determine the length of side DF and the unknown angle measures
In the given diagram, we have a right triangle.
We can determine the length of side DF by using the Pythagorean theorem
Consider triangle DEF, we can write that
|FE|² = |DE|² + |FD|²
(√45)² = (√35)² + |FD|²
45 = 35 + |FD|²
|FD|² = 45 - 35
|FD|² = 10
|FD| = √10
OR
|FD| = 3.1623
|FD| ≈ 3.2
To determine the measure of angle F, m ∠F, we can use SOH CAH TOA
We can write that
sin (F) = |DE| / |FE|
sin (F) = √35 / √47
Rationalize
sin (F) = (√35 × √47 )/ (√47 × √47 )
sin (F) = (√1645)/ (47)
sin (F) = 0.862949
F = sin⁻¹ (0.862949)
F = 59.649
F ≈ 59.6°
Thus, m ∠F ≈ 59.6°
m ∠F + m ∠E = 90° (Complementary angles)
59.6° + m ∠E = 90°
m ∠E = 90° - 59.6°
m ∠E ≈ 30.4°
Hence, the measure of angle E is approximately 30.4°
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A recent report indicated that 8 1/3% of all residents of a state did not have health insurance. What fraction of residents were uninsured
The given percentage is 8 1/3 %.
\(8\text{ }\frac{1}{3}\text{ \%=8}\frac{1}{3}\times\frac{1}{100}\)\(\text{ Use a}\frac{b}{c}=\frac{a\times c+b}{c}\text{.}\)\(=\frac{8\times3+1}{3}\times\frac{1}{100}\)\(=\frac{25}{3}\times\frac{1}{100}\)\(=\frac{1}{3}\times\frac{1}{4}\)\(=\frac{1}{12}\)\(8\text{ }\frac{1}{3}\text{ \%=}\frac{1}{12}\)
Hence 1/12 of residents were uninsured.
Castel spent half of his weekly allowance playing mini-golf. To earn more money his parents let him clean the gutters for $5.46. What is his weekly allowance if he ended with $12.66? His weekly allowance was $ ______
Answer:
18.12
Step-by-step explanation:
Not very clear what you mean. I added 5.46 and 12.66.
Simplify: 1/3(15y-6)
I NEED HELP PLZ!!!
Answer:
5y - 2
Step-by-step explanation:
1/3 ( 15y - 6 ) = (15y - 6) / 3 = 5y - 2
Done! Hope you learned how to do this/understood this and have a great day! Please mark me as brainliest, vote 5.0 on my answer and thank me to show some support! Bye!
a man has five pairs of socks, of which no two pairs are the same color. he randomly selects two socks from a drawer. what is the probability that he gets a matched pair? 118. bookshelf ord
The probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer is 5/45, or approximately 0.11.
To calculate the probability of the man getting a matched pair of socks when he randomly selects two socks from a drawer, we need to consider the number of possible combinations of socks that result in a match and divide that by the total number of possible combinations of two socks.
The man has a total of 5 pairs of socks, or 10 socks, so there are 10 choose 2, or 45, possible combinations of two socks. Out of these, 5 of them result in a match, because there are 5 pairs of matching socks in the drawer.
Therefore, the probability of getting a matched pair of socks is 5/45, or approximately 0.11. This means that there is an 11% chance that the man will select a matched pair of socks if he randomly selects two socks from the drawer.
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PLEASE HELP ME!
Diagram shows the distance time graph that represent Dendrick's journey Kl to vawang and David s journey from rawang to Kl. Both of them depart from the place at the same time
a) Calculate the length of time in minutes, David stop his car
b) If their journey starts at 9 am, what is the time david and dendrick
c) Calculate the speed in km h¯¹, of Dendrick when he meets David
Answer:
1) 45 minutes
2) they meet in 20 minutes
3) (12-6)/(20/60)=18kmh
Factor the polynomial x^2 + 4x + 4
solved it!!
If a ball is thrown directly upward with a velocity of 26 ft/s, its height (in feet) after t seconds is given by y-264-16. What is the maximum height attained by the bal? (Round your answer to the nea
If a ball is thrown directly upward with a velocity of 26 ft/s, then the maximum height attained by the ball is 225.5 feet
If a ball is thrown directly upward with a velocity of 26 ft/s, its height (in feet) after t seconds is given by:
y = -16t² + 26t + 264
The equation for the height of a ball thrown upward with a velocity of 26 ft/s is given by y = -16t² + 26t + 264.
We can find the maximum height attained by the ball using the following steps:
Step 1: Find the time at which the ball reaches maximum height. The maximum height occurs at the vertex of the parabola. The time taken to reach the vertex is given by:-b/2a = -26/(-32) = 0.8125 seconds.
Step 2: Substitute the time value into the equation to find the maximum height attained by the ball.
y = -16(0.8125)² + 26(0.8125) + 264= 225.5
Therefore, the maximum height attained by the ball is 225.5 feet (rounded to the nearest tenth of a foot).
The correct answer is 226 ft (rounded to the nearest foot).
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Melissa and Emily are playing at the pool.They have three different measuring jars for; liters, cups, and pints. They find that 7 cups of water and 3 liters of water filled 9.8 pints. Later, they find that if they start with 5 liters of water and remove 9 cups of water, they end up with 6 pints of water. Model the given two situations as a system of linear equations. Based on your equations, determine the relationship between;
Answer:
Here is the missing part.
Cups and liters:-1 litre = 2.1 cups
Cups and pints:- 1 pint = 2 cups
Pints and liters:-1 litre = 2.1 pints
Step-by-step explanation:
Step 1:
7 cups + 3 liters = 9.8 pints
\(7c+3l=9.8p\)
5 liters - 9 cups = 6 pints
\(5l+9c=6p\)
Cups and Liters
\(7c+3l=9.8p\)
\(p= 7c+3l/9.8\) (put in equation 2)
\(5l-9c= 7c+3l/9.8\\49l-88.2c=7c+3l\\49l-3l=7c-88.2c\\46l=45.2c\)
1 Liter = 2.1 Cups.
Step 2:
Cups and Pints
\(7c+3l=9.8p\\3l=9.8p-7c\)
\(l=9.8p-7c/3\)(put in equation 2)
\(5(9.8p-7c/3)-9c=6p\\(49p-35c/3)-9c=6p\\49/3p-35/3c-9c=6p\\49/3p-6p=35/3c+9c\\31/3p=62/3c\)
1 Pint = 2 Cups.
Step 3:
Pints and Liters
\(7c=9.8p-3l\)
\(c=9.8p-3l/7\)(put in equation 2)
\(5l-9(9.8p-3l/7)=6p\\5l-63/5p+27/7l=6p\\5l+27/7l=6p+63/5p\\62/7l=93/5p\)
1 Liter = 2.1 Pints.
does anybody know what 75% of $4 is
Answer:
$3
Step-by-step explanation:
Answer:
75% of $4 is $3
Step-by-step explanation:
Hope this helps
PLEASE HELP !
Is this correct ? help please !!!
Answer:
It is correct. It is correct.
Answer:
Step-by-step explanation:
Compare the expression 3 8 and 3 5 x 3 3 using the properties of multiplication what do you notice
Using the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power, it can be seens that that the two expressions are equal to each other.
The properties of multiplication state that when multiplying two expressions with the same base, we can add their exponents together. This means that 3 to the fifth power x 3 to the third power is equal to 3 to the eighth power.
In mathematical notation, this looks like:
3^8 = 3^5 x 3^3
Using the properties of multiplication, we can add the exponents together:
3^8 = 3^(5+3)
Simplifying the exponent:
3^8 = 3^8
This shows that the two expressions are equal to each other. Therefore, we can conclude that 3 to the eighth power and 3 to the fifth power x 3 to the third power are the same value.
Note: The question is incomplete. The complete question probably is: Use the properties of multiplication to compare the expressions 3 to the eighth power and 3 to the fifth power x 3 to the third power.
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Fungal Boiling Tea Inc. has fixed assets of $27,730. The company has long-term debt of $34,780 and note-payables (short-term) of $16,920, as well as stockholder equity of $5,875. What is the amount of net working capital
The amount of net working capital for the fixed assets of $27,730 and short term $16,920 is equal to option d) $4,935.
Fixed assets is equal to $27,730.
Long term debt is equal to $34,780
Short term = $16,920
Stockholder equity = $5,875
To calculate the net working capital,
we need to subtract current liabilities from current assets.
Current assets = Note-payables (short-term) + Stockholder equity
⇒Current assets = $16,920 + $5,875
⇒Current assets = $22,795
Current liabilities = Note-payables (short-term)
⇒Current liabilities = $16,920
Net working capital
= $27,730 - $22,795
= $4,935
Therefore, the amount of net working capital is option d) $4,935.
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2 5/12= -3 1/4 +k Find k Please and thank you!
The solution is of k = 17/3, using operations with mixed numbers in the context of this problem.
Mixed numbersA mixed number is modeled as follows:
a b/c.
In which:
a is the integer part of the number.b/c is the fractional part of the number.The fractional version of the number is as follows:
(ac + b)/c
Hence the fractional equivalent of the numbers in this problem are as follows:
2 5/12 = (2 x 12 + 5)/12 = 29/12.-3 1/4 = -(3 x 4 + 1)/4 = -13/4.The value of k is calculated as follows:
2 5/12= -3 1/4 +k
29/12 = -13/4 + k
k = 29/12 + 13/4
k = 29/12 + 39/12
k = (29 + 39)/12
k = 68/12
k = 34/6
k = 17/3.
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Please solve this equation: 3 + 4 = 21; 2 + 5 = 14; 7 + 7 = 98; 8 + 6 = ?
Answer:
112
Step-by-step explanation:
It appears that the relation is f(a, b) = a(a+b).
f(3, 4) = 3(3+4) = 21
f(2, 5) = 2(2+5) = 14
f(7, 7) = 7(7+7) = 98
f(8, 6) = 8(8+6) = 112
__
The symbol "+" has apparently been repurposed from its usual meaning in math. It is being used as an infix operator with two arguments. We have shown the relation above as a function f with two arguments (a, b). In our definition ...
f(a, b) = a(a+b)
the symbol "+" has its usual meaning.
_____
Additional comment
This sort of question requires a little bit of "out of the box" thinking. It helps immensely if you're familiar with your addition and multiplication facts. Then you are in a position to recognize how the outputs may be related to the inputs.
An airplane has a wingspan of 20 feet and a length of 15 feet. If the model of this airplane has a wingspan of 8 inches, what is the length of this model?
Answer:
The length of the model is 6 inches.
Step-by-step explanation:
The wingspan of the airplane and length of the airplane are a ratio of 4:3
The model is also supposed to be 4:3.
4:3 x 2 = 8:6
Or, 20x12=240
240/8=30
15x12=180
180/30=6.
Answer:
6 inches
Step-by-step explanation:
a family plans to have 3 children. for each birth, assume that the probability of a boy is the same as the probability of a girl. what is the probability that they will have three children of the same gender?
The probability that the family will have three children of the same gender is 1/4 or 25%.
To calculate the probability of having three children of the same gender, we can consider the possible outcomes for each child's gender.
Since the probability of having a boy or a girl is equal (assuming a 50% chance for each), we have two possible outcomes for each child: boy (B) or girl (G).
The total number of possible outcomes for the three children is 2 * 2 * 2 = 8, as each child has two possible genders.
Now, let's calculate the number of favorable outcomes where all three children have the same gender.
If they have all boys (BBB), there is only one favorable outcome.
If they have all girls (GGG), there is also only one favorable outcome.
Therefore, the total number of favorable outcomes is 1 + 1 = 2.
The probability of having three children of the same gender is then 2 favorable outcomes out of 8 possible outcomes, which can be expressed as 2/8 or simplified to 1/4.
So, the probability that the family will have three children of the same gender is 1/4 or 25%.
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What is the equation of the line through (-2,5) and (0, 3)?
Help please
y= -1 x + 4
found the slope and then rearranged y=mx+b to find b
lmk if you need any other help :)
how to calculate calculate mean and standard deviation after transforming a random variable combining random variables
to calculate calculate mean and standard deviation after transforming a random variable combining random variables, use the formulae for both the expected and standard deviation of such a linear combination with random variables.
What is standard deviation?Data dispersion in regard to the mean is quantified by a standard deviation, or "σ". Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.
Because it makes measures easier to comprehend when the data is spread, standard deviation is significant. The data's standard deviation will increase as the data's distribution becomes more widely scattered. The deviation of each observed value from the mean is measured using this metric. The majority of data in any distribution will fall within a 2 standard deviation range of the mean.
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The heights of the bars of a histogram correspond to _______ values. the heights of the bars of a histogram correspond to frequency values.
The heights of the bars of a histogram corresponding to frequency values.
This is further explained below.
What is the frequency?Generally, The number of instances of a recurring event that takes place in a certain amount of time is referred to as its frequency.
When compared to spatial frequency, it is sometimes referred to as temporal frequency, and when compared to angular frequency, it is sometimes referred to as ordinary frequency.
Both of these names stress the difference between the two types of frequency.
In conclusion, The heights of the individual bars in a histogram correspond to the frequency values being shown.
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when the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n = 100 will be a. wider than, b. narrower than, or c. equal to a confidence interval for a population mean based on a sample of n = 50.
This is because as the sample size increases, the confidence interval becomes more precise and thus narrower.
When the level of confidence and sample standard deviation remains the same, a confidence interval for a population mean based on a sample of n = 100 will be narrower than a confidence interval for a population mean based on a sample of n = 50. This is because larger sample sizes typically result in more precise estimates of the population mean, leading to a smaller margin of error and therefore a narrower confidence interval.
This is because as the sample size increases, the confidence interval becomes more precise and thus narrower.
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Danny’s dog weighs 45.33 pounds. His cat only weighs 14.89 pounds.
About how much more does his dog weigh?
Answer:
His dog weighs 30.44lbs more than his cat.
Step-by-step explanation:
The question asks how much more his dog weighs, so we use subtraction to find the answer.
a hospital administrator is interested to compare the average hospital stay at three hospitals in a certain city. the administrator collects random data for the length of hospital stay (in days) for the three hospitals. the administrator is interested to know if the average hospital stays are statistically the same for the three hospitals. use a significance level of 5%. the administrator has confirmed that the samples were randomly selected and independent, and the populations have normal distribution and the population variances are equal.
To determine if the average hospital stays are statistically the same for the three hospitals, a statistical test called ANOVA (Analysis of Variance) can be used. With a significance level of 5%, the null hypothesis is that the means of the three hospital stays are equal, while the alternative hypothesis is that at least one mean is different.
In this scenario, the administrator collects random data for the length of hospital stay from three hospitals in the city. Since the samples were randomly selected and independent, and the populations have normal distribution with equal variances, the conditions for performing an ANOVA test are satisfied.
ANOVA allows for comparing the means of multiple groups simultaneously. By conducting an ANOVA test, the administrator can determine if there are statistically significant differences among the average hospital stays in the three hospitals.
The test will calculate the F-statistic, which is the ratio of the between-group variability to the within-group variability. If the calculated F-statistic exceeds the critical value at the 5% significance level, it indicates that there are significant differences among the means.
If the ANOVA test results in rejecting the null hypothesis, indicating significant differences among the average hospital stays, the administrator can proceed with post-hoc tests to identify which specific hospital means differ from each other.
Overall, by utilizing the ANOVA test with the provided conditions and a significance level of 5%, the hospital administrator can determine if the average hospital stays are statistically the same or if there are significant differences among the three hospitals.
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If the bond angle between two adjacent hybrid orbitals is 180°, which is the hybridization?.
If the bond angle between two adjacent hybrid orbitals is 180 degree then the hybridization is sp hybridization , it forms linear molecules with an angle of 180°.
Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.
In sp hybridization, the s orbital of the excited state carbon is mixed with only one out of the three 2p orbitals. It is called sp hybridization because two orbitals (one s and one p) are mixed.
The resulting two sp hybrid orbitals are then positioned at 90 degree and 180 degree, respectively, with the two 2p unhybridized orbitals:
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What is the length, in feet, of the diagonal of a square with 8-foot sides? Round to the nearest tenth.
Answer:
11 feet
Step-by-step explanation:
Length of diagonal of square of side a = √2a
Here value of a = 8 feet
Therefore length of diagonal d = √2×8 = 1.414×8 = 11.312 feet
So after rounding to the nearest tenth the length of diagonal becomes 11 feet
Can someone help me asap? It’s due today
What simulation is a representation of independent events?
Answer:
Option 2 is a representation of independent events.
In option 2, the simulation involves randomly pulling a piece of hard candy out of a bag and eating it, then pulling out another piece. The act of pulling out one piece of candy does not affect the probability of pulling out another piece, as each piece is independent of the others.
In contrast, the other simulations involve dependent events. In option 1, the probability of selecting a slip of paper changes after each selection because the slips of paper are not replaced. In option 3, the probability of getting a certain outcome on the second spin is influenced by the outcome of the first spin. In option 4, the probability of selecting a certain card for the second draw is affected by which card was selected and removed from the deck in the first draw.
Step-by-step explanation:
Find the surface area of this triangular prism. Be sure to include the correct unit in your answer.
Answer:
816 square feet
Step-by-step explanation:
13(16+20+12) + 16(12) = 816
write an equation describing the relationship of the given variables. y varies inversely as the cube root of x and when x
The equation that describes the relationship between y and x is y = 30/(∛x).
Let's start by assigning the variables to their given values. We have y, which represents the dependent variable, and x, which represents the independent variable. We are told that y varies inversely with the cube root of x. Mathematically, we can express this relationship as:
y = k/(∛x)
In this equation, k represents the constant of variation. The constant of variation is a fixed value that relates the dependent variable (y) and the independent variable (x) in an inverse relationship. The cube root (∛) of x ensures that the relationship is inverse.
To find the specific equation that relates y and x, we need to determine the value of the constant of variation (k). We are given a specific point on the graph, where x = 216 and y = 5. We can use these values to solve for k.
Substituting the given values into the equation:
5 = k/(∛216)
To simplify this equation, we need to evaluate the cube root of 216:
∛216 = 6
Now we can substitute this value back into the equation:
5 = k/6
To solve for k, we can multiply both sides of the equation by 6:
5 * 6 = k
30 = k
Now we have determined the value of the constant of variation, k, which is 30. With this value, we can rewrite the equation that describes the relationship between y and x:
y = 30/(∛x)
This equation represents the inverse variation between y and the cube root of x. As x changes, y will vary inversely with the cube root of x, with the constant of variation, k, equal to 30.
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Complete Question:
Write an equation describing the relationship of the given variables.
y varies inversely as the cube root of x and when x = 216, y = 5.
can someone help me with this
Answer:
RQ
Step-by-step explanation:
Since there are congruent, they are mirrored.
Which of the following is a characteristic of alternate exterior angles formed by a transversal intersects a pair of parallel lines?
A. The alternate exterior angles are always supplementary.
B. The alternate exterior angles are always congruent.
C. The measures of the alternate exterior angles are always different.
D. The alternate exterior angles are always complementary.
Answer:
B
Step-by-step explanation:
We are to select which out of the options best answer the question. The correct answer is that alternate exterior angles are congruent.
Whenever we are talking about alternate angels, we are talking about two angles which forms ‘z’ letter , given two parallel lines and a transversal passing the lines. Now while the alternate angles are the angles at the corner of the z, the exterior alternate angles are the angles which are above the first parallel line and below the second parallel line.
Please check attachment for what is meant by exterior alternate angles
Jaidee and Beth each improved their yards by planting rose bushes and ivy. They bought their supplies from the same store. Jaidee spent $140 on 2 rose bushes and 12 pots of ivy. Beth spent $120 on 6 rose bushes and 6 pots of ivy. What is the cost of one rose bush and the cost of one pot of ivy?
The cost of one rose bush is $10 and the cost of one pot of ivy is $10.
Let's assume the cost of one rose bush is represented by "R" and the cost of one pot of ivy is represented by "I".
According to the given information:
Jaidee spent $140 on 2 rose bushes and 12 pots of ivy:
2R + 12I = 140 ...(1)
Beth spent $120 on 6 rose bushes and 6 pots of ivy:
6R + 6I = 120 ...(2)
We now have a system of two equations with two variables. To solve this system, we can use either substitution or elimination method. Let's use the elimination method.
Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of "R" in both equations equal:
6R + 36I = 420 ...(3)
12R + 12I = 240 ...(4)
Now, subtract equation (4) from equation (3):
(6R + 36I) - (12R + 12I) = 420 - 240
-6R + 24I = 180 ...(5)
Now we have a new equation (5) that relates "R" and "I".
Let's solve equations (5) and (2) together:
-6R + 24I = 180 ...(5)
6R + 6I = 120 ...(2)
Add equation (5) and equation (2):
(6R - 6R) + (24I + 6I) = 180 + 120
30I = 300
Divide both sides of the equation by 30:
I = 10
Now substitute the value of "I" into equation (2) to find the value of "R":
6R + 6(10) = 120
6R + 60 = 120
6R = 120 - 60
6R = 60
Divide both sides of the equation by 6:
R = 10
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