The accumulated amount 54675 ([tex]2.7^{t}\\[/tex]) in dollars of an account with an initial deposit of $7,500 and earns 3. 4% compound interest semi-annually.
A compound interest is calculated by the formula,
[tex]A = P [ 1 + ( r/n )]^{nt}[/tex]
where, A is the accumulated amount at the end of the period ,
P is the initial amount of deposit,
r is the rate of interest earned on the initial deposit in the period
t is the time periods elapsed
and n is the number of times interest is applied per time period
Here the account has an initial deposit , P = $7500 and earns 3.4% rate of interest, say r, compounded semi- annually, that is n= 2 ( as rate of interest is applied twice a year or twice per time period) in time period, say t.
Therefore by the formula of compound interest we get,
Accumulated amount, A = [tex]7500[ 1 + 3.4/2]^{2t}[/tex]
⇒ A = [tex]7500[ 1 + 1.7]^{2t}[/tex] in dollars
⇒ A = [tex]7500(2.7)^{2t}[/tex] in dollars
⇒ A = 7500 (2.7)² ([tex]2.7^{t}[/tex] ) in dollars
⇒ A = 54675 ([tex]2.7^{t}\\[/tex]) in dollars
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5PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Answer:
b. sin X and c. cos Y
Step-by-step explanation:
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
sin Y = 32/40 incorrect
sin X = 24/40 correct
cos Y = 24/40 correct
cos X =32/40 incorrect
So the answers are sin X and cos Y
If c is the number that satisfies the conclusion of the Mean Value Theorem for f(x)= x^3 - 2x^2 on the interval 0â¤xâ¤2, then c=a) 0b) 1/2c) 1d) 4/3
This means that c must be 1/2, since it is the only value in the interval (0,2) where f'(c) = -1/2, which satisfies the equation given by the Mean Value Theorem.
To apply the Mean Value Theorem, we need to check if f(x) is continuous on [0,2] and differentiable on (0,2).
[tex]f(x) = x^3 - 2x^2[/tex] is a polynomial function, so it is continuous and differentiable everywhere.
Now, we can use the Mean Value Theorem, which states that there exists a number c in (0,2) such that:
[tex]f'(c) = (f(2) - f(0))/(2-0)[/tex]
First, let's find f'(x):
[tex]f'(x) = 3x^2 - 4x[/tex]
Now, we can solve for c:
f'(c) = 3c^2 - 4c
f(2) = 2^3 - 2(2^2) = -4
f(0) = 0^3 - 2(0^2) = 0
(f(2) - f(0))/(2-0) = -4/2 = -2
So, we need to solve the equation 3c^2 - 4c = -2 for c.
Rearranging, we get:
3c^2 - 4c + 2 = 0
Using the quadratic formula, we get:
c = (4 ± sqrt(16 - 24))/6
c = (4 ± 2i)/6
Since the interval is [0,2], we only need to consider real solutions.
[tex]f'(c) = 3c^2 - 4c\\f(2) = 2^3 - 2(2^2) = -4\\f(0) = 0^3 - 2(0^2) = 0\\(f(2) - f(0))/(2-0) = -4/2 = -2\\[/tex]
Therefore, c = 4/3 is not a valid solution.
To choose between the remaining options, we can test if f'(c) is positive or negative.
For c = 0, f'(0) = 0 - 0 = 0.
For [tex]c = 1/2, f'(1/2) = 3(1/2)^2 - 4(1/2) = -1/2.[/tex]
For[tex]c = 1, f'(1) = 3(1)^2 - 4(1) = -1.[/tex]
Therefore, f'(c) is negative on the interval [0,1/2] and positive on the interval [1/2,2].
This means that c must be 1/2, since it is the only value in the interval (0,2) where f'(c) = -1/2, which satisfies the equation given by the Mean Value Theorem.
Therefore, the answer is (b) 1/2.
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A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
The best prediction is that the college will have about 480 students who prefer cookies.
To solve this problem
According to the table, 27 out of 225 students prefer cookies. To find the prediction for the number of cookies the college will need, we can set up a proportion:
27/225 = x/4000
Where x is the predicted number of students who prefer cookies.
Solving for x, we get:
x = (27/225) * 4000
x ≈ 480
Therefore, the best prediction is that the college will have about 480 students who prefer cookies.
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1. Suppose that angle AOC, a central angle of a circle, and angle ABC, an inscribed angle of the same circle, intercept the same arc. Circle the correct word(s) in the sentence. The measure of angle AOC is [half | equal to | double] the measure of angle ABC.
Answer:
The measure of angle AOC is double the measure of angle ABC.
Step-by-step explanation:
You want to know the relationship between central angle AOC in circle O and inscribed angle ABC subtending the same arc AC.
Inscribed angleThe measure of an inscribed angle is half the measure of the arc it intercepts. The measure of a central angle is exactly equal to the measure of the arc it intercepts. (That's how the arc measure is determined.)
Hence, the measure of angle AOC is double the measure of angle ABC.
__
Additional comment
Inscribed : central = 1 : 2
Central : inscribed = 2 : 1
You need to be a little careful of the wording of the relationship. Which is double and which is half can be confused when it's written in words. On a diagram, the angle with its vertex in the center will obviously be larger than the one with its vertex on the circle.
you are given a 100-meter-long rope, and you need to measure a length of 10 meters without any measuring devices. you can only fold or manipulate the rope, but you cannot cut or mark it. how can you measure 10 meters accurately?
To measure a length of 10 meters without any measuring devices from 100 meters rope is fold the rope ten times and 10th fold of 100 m rope is equals to 10 m.
Total Length of rope = 100 meters
We need to measure a length of 10 meters without using any measuring devices. The ways that we can use to measure the required length includes only fold or manipulate the rope, but you cannot cut or mark it. Now, we use the division arithmetic operation to measure the length. The factors of 100 is written as 100 = 2×2× 5×5 = 10× 10
If we divide 100 by 10 then results 10 as quotient and 0 as remainder. So, the rope with length 100 meters is divided into 10 parts of 10 meters length of rope. But we cannot cut the rope, so folds the rope ten times ( i.e, first half -half then again half into half-half). Therefore, the last fold is measure of length 10 meters.
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PLEASWWW HELP ITS VERY MUCH APPRECIATED!!
Well, a diameter is double the radius. The radius is given in the image.
So, 2+2 = 4
1. Calculate the area of the following parallelogram:
28 in²
26 in²
40 in²
30 in
The area of the parallelogram shown in the figure is 30 in². Option D is correct.
The area of the parallelogram is given by the following formula,
Area = base * height,
From the figure we have base = 10 in and height = 3 in
So area can be given as,
Area = 10 * 3
Area = 30 in²
Thus, the area of the parallelogram shown in the figure is 30 in².
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the _____ (if any) are determined by the values of x that make f(x)=0. to find them, solve the quadratic equation:
The roots (if any) are determined by the values of x that make f(x) = 0. To find them, we solve the quadratic equation associated with the function.
A quadratic equation is an equation of the form:
ax² + bx + c = 0
where a, b, and c are constants. For a quadratic function of the form:
f(x) = ax² + bx + c
the roots are the values of x that satisfy the equation f(x) = 0. To find the roots, we set f(x) equal to zero and solve for x using the quadratic formula:
x = (-b ± √(b² - 4ac))/2a
If the discriminant (b² - 4ac) is negative, then the quadratic equation has no real roots, and the function f(x) does not intersect the x-axis. If the discriminant is zero, then the quadratic equation has one real root, and the function f(x) touches the x-axis at that point. If the discriminant is positive, then the quadratic equation has two real roots, and the function f(x) intersects the x-axis at those points.
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URGENT! Will give brainliest :)
Rosa recorded the height (in centimeters) of a pea plant over a 10-day period for a science experiment. Which equation is the best model of the data?
A. y= 2.2 - (1.1%)
B. y= 0.5x + 1.8
C. y= 2.0 • (1.4%)
D. y = 0.7 x + 2.1
According to this research, options B and D appear to be the most slope plausible explanations for the data. However, without the real data, determining which equation is the best model is impossible.
what is slope?The slope of a line indicates how steep it is. The gradient's mathematical equation is known as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7.The slope of the line is m. b is b at the y-intercept, and (0, b).
It is impossible to establish which equation is the best model of the data without the actual data. However, we may analyse each possibility based only on the facts provided:
A. y= 2.2 - (1.1%): This equation appears to contain a constant term and a negative slope, making it unsuitable for predicting plant height over time.
B. y= 0.5x + 1.8: The positive slope of this equation indicates that the plant's height rises with time. The constant term of 1.8 might represent the plant's beginning height, while the coefficient of 0.5 could reflect the plant's growth rate.
C. y= 2.0 • (1.4%): This equation appears to contain a constant term and a positive slope, but the percentage term is not obvious how it links to the data.
D. y = 0.7 x + 2.1: This equation, like option B, has a positive slope and a constant term. The coefficient of 0.7 might reflect the plant's growth rate, while the constant term of 2.1 could represent the plant's original height.
According to this research, options B and D appear to be the most plausible explanations for the data. However, without the real data, determining which equation is the best model is impossible.
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The ratio of girl to boys in mr Day class is 3 to 5 . If there is 15 boys in mr Day class how many more boyz are there then girls
Answer:
If there are 15 boys in Mr. Day’s class and the girl to boy ratio is 3 to 5, then there are 9 girls in Mr. Day’s class. To find out how many more boys there are than girls, you can subtract the number of girls from the number of boys:
15 boys - 9 girls = 6 more boys than girls.
Step-by-step explanation:
33. Find the surface area of the rectangular prism.
7 cm
12 cm
1.6 cm
Answer: 228.8cm
Step-by-step explanation:
Hope this helps! :)
In this diagram, AT = 2x + 3, CT = 3x - 1, BT = x + 5,
DT = 4x + 1, and mLATD = 41x + 8. If x = 2,
which segment is the perpendicular bisector of the other? Explain your reasoning.
Answer:
CT is the perpendicular bisector of AB
Step-by-step explanation:
calculate the segments using x = 2
AT = 2x + 3 = 2(2) + 3 = 4 + 3 = 7
BT = x + 5 = 2 + 5 = 7
thus AT = BT
CT = 3x - 1 = 3(2) - 1 = 6 - 1 = 5
DT = 4x + 1 = 4(2) + 1 = 8 + 1 = 9
thus CT ≠ DT
∠ ATD = 41x + 8 = 41(2) + 8 = 82 + 8 = 90°
Thus CT is the perpendicular bisector of AB
The ratio of cars to people in one country is 300 to 1,000. Write a fraction to represent this ratio in simplest form
Answer:
3/10
Step-by-step explanation:
what is the missing number. Good points
Answer:
Which number is missing?
40 38 35 31 26 20 13 5
Pattern: ( -2, -3, -4, etc)
40 - 2 = 38
38 - 3 = 35
35 - 4 = 31
31 - 5 = 26
26 - 6 = 20
20 - 7 = 13
13 - 8 = 5
Step-by-step explanation:
You're welcome.
Determine the solutions to the equation x^2 = 4x + 41.
Answer:
The solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).
Step-by-step explanation:
To solve the equation x^2 = 4x + 41, we can first rearrange it as x^2 - 4x - 41 = 0.
Next, we can use the quadratic formula:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
where a, b, and c are the coefficients of the quadratic equation. In this case, a = 1, b = -4, and c = -41.
Substituting these values into the formula, we get:
x = (4 ± sqrt((-4)^2 - 4(1)(-41))) / 2(1)
Simplifying:
x = (4 ± sqrt(176)) / 2
x = (4 ± 4sqrt(11)) / 2
x = 2 ± 2sqrt(11)
Therefore, the solutions to the equation x^2 = 4x + 41 are x = 2 + 2sqrt(11) and x = 2 - 2sqrt(11).
research conducted a few years ago showed that 12% of uw-platteville students had traveled outside the us. uw-platteville has recently implemented a new study abroad program and results of a new survey show that out of the 100 randomly sampled students 35 have traveled abroad. to know if the proportion of students at uw-platteville who have traveled abroad has increased after the implementation of the study abroad program, what is the appropriate null and alternative hypothesis?
The null hypothesis is that the proportion of students who have traveled abroad is still 12%, while the alternative hypothesis is that the proportion has increased and is now greater than 12%.
The appropriate null hypothesis is that the proportion of students at UW-Platteville who have traveled abroad remains the same as before the implementation of the study abroad program. The alternative hypothesis is that the proportion of students who have traveled abroad has increased after the implementation of the program.
Mathematically:
H0: p = 0.12
Ha: p > 0.12
where p is the true proportion of students at UW-Platteville who have traveled abroad.
To test this hypothesis, we can use a one-tailed z-test for proportions. Using the given sample information, we can calculate the test statistic as:
z = (0.35 - 0.12) / sqrt((0.12 * 0.88) / 100) = 3.87
where 0.88 is the complement of 0.12, and sqrt denotes the square root. The critical value for a one-tailed test at the 0.05 level of significance is 1.645.
Since the test statistic (3.87) is greater than the critical value (1.645), we reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level to support the claim that the proportion of students who have traveled abroad has increased after the implementation of the study abroad program.
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At the game, the Junior class sold slices of pizza for $.75 each and hamburgers for $1.35 each. They sold 40 more slices of pizza than hamburgers and their sales totaled $292.50. How many slices of pizza did they sell
The Junior class sold 165 slices of pizza.
Let x represent the number of hamburgers sold and y represent the number of slices of pizza sold.
The total amount from sales: 1.35x + 0.75y = 292.50
They sold 40 more slices of pizza than hamburgers: y = x + 40
Now, we'll solve the system of equations using the substitution method:
Substitute the second equation into the first equation:
1.35x + 0.75(x + 40) = 292.50
Distribute $0.75 through the parentheses:
1.35x + 0.75x + 30 = 292.50
Combine like terms:
2.10x + 30 = 292.50
Subtract 30 from both sides of the equation:
2.10x = 262.50
Divide both sides by 2.10 to solve for x:
x = 125
Now that we know there were 125 hamburgers sold, we can use the second equation to find the number of slices of pizza sold:
y = x + 40
y = 125 + 40
y = 165
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O is the center of the regular pentagon below. Find its area. Round to
the nearest tenth if necessary.
14
The area of the regular pentagon is 490 square units
How to determine the area of the pentagonThe formula used for calculating the area of a regular pentagon is expressed with the equation
A = 1/2 pa
Such that the parameters are;
A is the area of the pentagon.p is the perimeter of the pentagon.a is the apothem.From the information given, we have that;
Perimeter = 5s
Substitute the values,
Perimeter = 5(14)
multiply the values
Perimeter = 70 units
Now, substitute the value into the formula
Area = 1/2 × 70(14)
Area = 980/2
Divide the values
Area = 490 square units
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Answer step by step due tmrw
The interior angles measure 160° and the exterior measure 200°
How to find the angles?The sum of the interior angles of a polygon of n sides is:
(n - 2)*180
here n = 18
(18 - 2)*180 = 2880
divide that by the number of sides
2880/18 = 160°
That is the measure of each interior angle, and the exteriors are such that the sum is 360, then:
a + 160 = 360
a = 360 - 160 = 200
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The function f(x)=log0. 75x is decreasing.
True or false
A statement 'The function f(x)=log0. 75x is decreasing' is True.
We know that a function, y = f(x) is a decreasing function when (dy/dx) ≤ 0 for all such values of interval (a, b).
Consider a function f(x)=log(0.75^x)
We write a function f(x) as,
f(x) = log(0.75^x)
f(x) = log[(3/x)^x]
f(x) = log([tex]\frac{3^x}{4^x}[/tex])
Now we find the derivative of above function with respect to x.
f'(x) = d/dx [ log([tex]\frac{3^x}{4^x}[/tex])]
f'(x) = [tex]1/(\frac{3^x}{4^x} )[/tex] [d/dx ([tex]\frac{3^x}{4^x}[/tex])]
f'(x) = [tex](\frac{4^x}{3^x})[\frac{4^x[3^xlog(3)]-3^x[4^xlog(4)]}{4^{2x}} ][/tex]
f'(x) = log(3) - log(4)
f'(x) = -0.1249
f'(x) < 0
So, the function f(x) is a decreasing function.
Thus the statement is True.
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solve for x
khan academy solve similar triangles advanced
Value of side CD = x=3
What is similarity of two triangle ?When two triangles are are referred to as similar figures when they share the same shape but different in size.
given that CB and ED are perpendicular to AD,
in triangle ABC and ADE
∠A=∠A (common angle )
∠B=∠D (both are 90 degree)
ΔABC≈ ΔADE by angle-angle similarity .
and we know that when two triangle are similar then their corresponding sides are with in the same ratio or proportional.
so ,here we proved that triangle ABC and ADE are similar,
then ,
[tex]\frac{BC}{ED}=\frac{AB}{AD}[/tex]
[tex]\frac{x}{5}=\frac{9}{9+6}[/tex]
[tex]\frac{x}{5} =\frac{9}{15}\\ X=3[/tex]
x=3
from above result ,value of side CB =x=3
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A packet of chips cost $9.99 if the price decreases by 12% what will the new price be
If the price of the packet of chips decreases by 12%, the new price will be:
New price = $9.99 - (12/100) x $9.99
New price = $9.99 - $1.199
New price = $8.791
Therefore, the new price of the packet of chips will be $8.791.
Pls help for 10 pts :)) (Caeser Cipher)
The sixth and seventh letters "NO" become the 15th and 14th letters in the alphabet respectively when shifted by 11 positions, decrypt to "E" and "N" respectively. Therefore, the decrypted plaintext is "CSPAEN".
what is decrypted plaintext ?
The decrypted plaintext is the original message that was encrypted using a cipher, which has now been converted back to its original form using the appropriate decryption technique.
In the given question,
The given ciphertext "ZYJGKNO" can be decrypted using a times-11 cipher as follows:
The first letter "Z" becomes the third letter in the alphabet when shifted by 11 positions, so it decrypts to "C".
The second letter "Y" becomes the 24th letter in the alphabet when shifted by 11 positions, so it decrypts to "T".
The third letter "J" becomes the 18th letter in the alphabet when shifted by 11 positions, so it decrypts to "S".
The fourth and fifth letters "GK" become the 16th and 10th letters in the alphabet respectively when shifted by 11 positions, so they decrypt to "P" and "A" respectively.
The sixth and seventh letters "NO" become the 15th and 14th letters in the alphabet respectively when shifted by 11 positions, so they decrypt to "E" and "N" respectively.
Therefore, the decrypted plaintext is "CSPAEN".
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For which of the following compound inequalities is there no solution?
The compound inequality that has no solution is d) m + 9 < 8 and -2m ≥ 10.
What is compound inequality?A compound inequality combines two or more inequalities using the logical connectives "and" or "or".
Compound inequalities are used to describe a range of values that satisfy multiple conditions simultaneously.
In the given compound inequality, the first inequality states that m + 9 is less than 8, which can be rewritten as m < -1.
The second inequality states that -2m is greater than or equal to 10, which can be rewritten as -2m ≥ 10.
However, the two inequalities cannot be true at the same time because if m is less than -1, then -2m would be greater than 2, and therefore cannot be greater than or equal to 10.
So there is no value of m that satisfies both inequalities simultaneously, resulting in no solution.
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of 100 patients selected at random from a clinic, 33 were found to have high blood pressure. construct a 95% confidence interval for the percentage of all patients at this clinic that have high blood pressure.
We can say with 95% certainty that the genuine rate of all patients at this clinic who have high blood pressure is between 24% and 42%.
To develop a 95% certainty interim for the rate of all patients at this clinic that have tall blood weight, we will utilize the equation:
CI = p ± z*(p*(1-p)/n))
where p is the sampling extent, z is the z-score related to the required certainty level (in this case, 1.96 for 95% certainty), and n is the test measure.
We are given that out of a test of 100 patients, 33 have high blood weight. In this manner, the test extent is:
p = 33/100 = 0.33
Utilizing the equation over, we will calculate the edge of the mistake:
Arduino
ME = z*(p*(1-p)/n)) = 1.96*(0.33*(1-0.33)/100)) ≈ 0.09
At that point, we are able to develop the 95% certainty interim:
CI = p ± ME = 0.33 ± 0.09 = (0.24, 0.42)
Hence, able to say with 95% certainty that the genuine rate of all patients at this clinic who have high blood weight is between 24% and 42%.
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What is one subtracted by 3/7
Answer:
4/7
Step-by-step explanation:
1-3/7
7/7 -3/7
4/7
What is the power of the hypothesis test, using the decision rule given above, if the population mean amount of mercury is 11.5 micrograms per ounce? Give your answer to 4 decimal places.
The true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.
In hypothesis testing, the power of a test refers to the probability of correctly rejecting a false null hypothesis.
To calculate the power of a test, we need to know the significance level of the test, the sample size, the effect size, and the variance of the population.
Additionally, we need to know the specific hypothesis being tested, as the decision rule and power calculation depend on the null and alternative hypotheses.
A hypothesis test for the population mean amount of mercury in a certain type of fish.
Test whether the mean amount of mercury is different from 11.5 micrograms per ounce, using a two-tailed test at a significance level of 0.05.
If the sample size is 100, the effect size is 0.5, and the population variance is 4, then the power of the test is approximately 0.7629.
This means that if the true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.
The hypothesis test, it is impossible to calculate the power.
It is essential to know the specific hypothesis being tested, as well as the details of the test, such as the sample size, effect size, and variance.
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Which angle is supplemental to angle 6?
Select one:
a.
Angle 8
b.
Angle 2
c.
Angle 7
d.
Angle 3
Supplementary angles are angles that add up to 180°. Angle 6 is a right angle, so it's worth 90°. This means that the other angle(s) have to be 90° as well.
As you can see, the other angle with 90° is angle 3, thus, making it the correct answer.
Kylie brought 5 pears to soccer practice to share with her teammates. She cuts each pear into thirds. How many slices of pears does she have to share with her teammates? Which equations can you use to solve the problem? Select two equations. A. 5 × 3 = 15 B. 1 5 × 1 3 = 1 15 C. 1 5 × 3 = 3 5 D. 5 ÷ 1 3 = 15 E. 1 3 ÷ 5 = 1 15 answer quick please
Answer:
Eqation a and 15
Step-by-step explanation:
because 5 pears all cut into thirds is 15 slices 5 times 3 is 15
Find the missing measures in a circle in a square
The measure of the missing angle in the cyclic quadrilateral is 104°
Circle Geometry: Calculating the measure of the inscribed angleFrom the question, we are to determine the measure of the inscribed angle in the given diagram
In the given diagram, we have a cyclic quadrilateral.
From one of the circle theorems, we known that
The sum of the opposite angles of cyclic quadrilateral are supplementary. That is they sum up to 180 degrees.
Let the unknown angle measure be x,
Then,
We can write that
x + 76° = 180°
x = 180° - 76°
x = 104°
Hence, the missing angle measure is 104°
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