Answer:
Step-by-step explanation:
The probability of getting exactly 25 heads in 50 coin flips would be higher than flipping a coin 6 times and getting exactly 3 heads.
To understand why, we can use the formula for calculating the probability of getting a specific number of heads in a given number of coin flips, which is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where P(X=k) is the probability of getting exactly k heads, n is the total number of coin flips, p is the probability of getting heads on a single coin flip, and (n choose k) is the binomial coefficient.
For the first scenario of flipping a coin 50 times and getting exactly 25 heads, we can plug in the values and get:
P(X=25) = (50 choose 25) * 0.5^25 * 0.5^25 = 0.112
For the second scenario of flipping a coin 6 times and getting exactly 3 heads, we can similarly plug in the values and get:
P(X=3) = (6 choose 3) * 0.5^3 * 0.5^3 = 0.3125
As we can see, the probability of getting exactly 25 heads in 50 coin flips is much higher than the probability of flipping a coin 6 times and getting exactly 3 heads. This is because the probability of getting a single head on a coin flip is 0.5, and as the number of coin flips increases, the probabilities of different outcomes converge towards a bell-shaped distribution centered around 0.5. This means that the probability of getting a specific number of heads in a large number of coin flips becomes more likely as the number of coin flips increases.
PLEASE help solving these 2 problems
Answer:
42° and 95°
Step-by-step explanation:
1
the inscribed angle EFD is half the measure of its intercepted arc , that is
∠ EFD = [tex]\frac{1}{2}[/tex] × DE = [tex]\frac{1}{2}[/tex] × 84° = 42°
2
ABCD is a cyclic quadrilateral.
the opposite angles sum to 180° , that is
∠ B + ∠ D = 180°
∠ B + 85° = 180° ( subtract 85° from both sides )
∠ B = 95°
I need help! 25 brainly points!
The surface areas for each figures are:
220 ft² 410 cm²596 cm²360 cm²Surface area of cylinders include: 132π mm²22π ft²396π square inches.How to calculate surface areas?1. The surface area of the cuboid is:
Top and bottom: 2(10 ft x 4 ft) = 80 ft²
Front and back: 2(10 ft x 5 ft) = 100 ft²
Sides: 2(4 ft x 5 ft) = 40 ft²
Total surface area = 80 + 100 + 40 = 220 ft²
2. The surface area of the cuboid is:
Top and bottom: 2(18 cm x 5 cm) = 180 cm²
Front and back: 2(18 cm x 5 cm) = 180 cm²
Sides: 2(5 cm x 5 cm) = 50 cm²
Total surface area = 180 + 180 + 50 = 410 cm²
3. The surface area of the prism is:
Top and bottom: 2(5 cm x 14 cm) = 140 cm²
Front and back: 2(5 cm x 12 cm) = 120 cm²
Sides: 2(12 cm x 14 cm) = 336 cm²
Total surface area = 140 + 120 + 336 = 596 cm²
4. The surface area of the stacked cuboids is:
Top and bottom of first cuboid: 2(6 cm x 7 cm) = 84 cm²
Front and back of first cuboid: 2(6 cm x 2 cm) = 12 cm²
Sides of first cuboid: 2(7 cm x 2 cm) = 28 cm²
Front and back of second cuboid: 2(7 cm x 2 cm) = 28 cm²
Sides of second cuboid: 2(2 cm x 4 cm) = 8 cm²
Front and back of third cuboid: 2(2 cm x 10 cm) = 40 cm²
Sides of third cuboid: 2(10 cm x 8 cm) = 160 cm²
Total surface area = 84 + 12 + 28 + 28 + 8 + 40 + 160 = 360 cm²
5. The surface area of the cylinder is:
Top and bottom: 2π(6 mm)² = 72π mm²
Side: 2π(6 mm)(5 mm) = 60π mm²
Total surface area = 72π + 60π = 132π mm²
6. The surface area of the cylinder is:
Top and bottom: 2π(1 ft)² = 2π ft²
Side: 2π(1 ft)(10 ft) = 20π ft²
Total surface area = 2π + 20π = 22π ft²
7. The surface area of the cylinder stacked on a cube is:
Top and bottom of cylinder: 2π(5 m)² = 50π m²
Side of cylinder: 2π(5 m)(8 m) = 80π m²
Surface area of cube: 6(10 m x 13 m) = 780 m²
Total surface area = 50π + 80π + 780 = (130π + 780) m²
8. The surface area of the cylinder is:
Top and bottom: 2π(9 in)² = 162π in²
Side: 2π(9 in)(4 in) = 72π in²
Therefore, the total surface area of the cylinder is:
2(162π in²) + 72π in² = 396π in²
So the surface area of the cylinder is 396π square inches.
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Image transcribed:
Find the surface area of each figure.
10 ft
18 cm
5 cm
4 ft
5 ft
3.
4.
6 cm
7 cm
2 cm
5 cm
12 cm
14 cm
4 cm
10 cm
8 cm
Find the surface area of each cylinder. Leave your answer in terms of π.
5.
6 mm
6.
1 ft
5 mm
10 ft
7.
5 m
8.
4 in.
8 m
10 m
9 in.
13 m
11 m
247
Journal and Practice Workbook
Geometry
I need help with this problem
The area of the region below y = x^2 + x + 4 and above y = 2 for 2 <= x <= 6 is 93.33 square units.
Finding the area of the regionTo find the area of the region below y = x^2 + x + 4 and above y = 2 for 2 <= x <= 6, we need to integrate the difference between the two functions with respect to x over the given interval.
The lower boundary of the region is y = 2, and the upper boundary is y = x^2 + x + 4. So, we can write the integral as:
∫[2,6] [(x^2 + x + 4) - 2] dx
Simplifying the integrand, we get:
∫[2,6] (x^2 + x + 2) dx
Integrating with respect to x, we get:
[(1/3)x^3 + (1/2)x^2 + 2x] evaluated from 2 to 6
Plugging in the upper and lower limits, we get:
[(1/3)(6^3) + (1/2)(6^2) + 2(6)] - [(1/3)(2^3) + (1/2)(2^2) + 2(2)]
Simplifying the expression, we get:
93
Therefore, the area of the region is 93.33 square units.
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How do you simplify 9z³ + 19u ?
Answer: 172z + 19u
Step-by-step explanation: To look up to the power of, use: "^"
2^6
4^5 etc.
In a study of the effects of a 1977 dioxin spell in Italy on the ratio of male babies to female babies born to humans, researchers wanted to know whether dioxin exposure affected the ratio in the seven years following the spill the researchers found that the of the 123 babies born to parents in the affected region 51 warm out the ratio of males to females in previous period during which exposure to dioxin was pretty presume to be absent. What is 0.52 for the researchers conducted the hypothesis test to determine whether the The later ratio is different from the earlier ratio. What does making a type two error mean in the context of this hypothesis test
The value of 0.52 represents the ratio of male babies to female babies born in the affected region in the seven years following the 1977 dioxin spill.
To conduct a hypothesis test to determine whether this ratio is different from the earlier ratio, we can set up the null and alternative hypotheses as follows:
Null hypothesis (H0): The ratio of male babies to female babies in the affected region did not change significantly after the 1977 dioxin spill.
Alternative hypothesis (Ha): The ratio of male babies to female babies in the affected region changed significantly after the 1977 dioxin spill.
We can use a one-sample proportion test to test this hypothesis. The test statistic is calculated as:
z = (p - P₀) / √(P₀ * (1 - P₀) / n)
where p is the sample proportion (0.52), P0 is the hypothesized population proportion (0.51), and n is the sample size (123).
Using a significance level of 0.05, we can compare the calculated test statistic to the critical value from the standard normal distribution. If the calculated test statistic falls outside the critical values, we reject the null hypothesis in favor of the alternative hypothesis.
A type II error in this context would occur if we fail to reject the null hypothesis when it is actually false. In other words, we would conclude that the ratio of male babies to female babies did not change significantly after the dioxin spill, when in fact it did. This means that we would fail to detect a real effect of dioxin exposure on the ratio of male to female births, which could have important implications for public health and environmental policy.
Steps:
1) State the null and alternative hypotheses
2) Choose a significance level (alpha)
3) Calculate the test statistic
4) Determine the critical value from the standard normal distribution based on the chosen alpha level
5) Compare the calculated test statistic to the critical value
6) Make a decision to either reject or fail to reject the null hypothesis
7) Interpret the results and draw conclusions, including the possibility of a type II error.
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Question:
In a study of the effects of a 1977 dioxin spell in Italy on the ratio of male babies to female babies born to humans, researchers wanted to know whether dioxin exposure affected the ratio in the seven years following the spill the researchers found that the of the 123 babies born to parents in the affected region 51 warm out the ratio of males to females in previous period during which exposure to dioxin was pretty presume to be absent.
What is 0.52 for the researchers conducted the hypothesis test to determine whether the later ratio is different from the earlier ratio? What does making a type two error mean in the context of this hypothesis test?
What is this
I have no idea what this is
Answer:
m = 2Dn = abStep-by-step explanation:
You want the formula for angle C in triangle ABC with area D.
Area formulaThe relevant formula for the area of the triangle is ...
Area = 1/2ab·sin(C)
When the area is D, this is ...
D = 1/2ab·sin(C)
RearrangeYou are being asked to rearrange the formula to give an expression for C.
2D/(ab) = sin(C) . . . . divide by the coefficient of sin(C)
[tex]C=\sin^{-1}\left(\dfrac{2D}{ab}\right)=\sin^{-1}\left(\dfrac{m}{n}\right)[/tex]
Comparing parts of the expressions, we see that ...
m = 2Dn = a·bHELP Find x assuming segments are tangent
The radius x for the circle is derived to be 10.92 using the Pythagoras rule for the right triangle.
How to evaluate for the radius using Pythagoras ruleSince the line with length 12 is tangent to the circle, then the triangle is a right triangle and the Pythagoras rule can be applied as follows:
x² + (x + 6)² = 12²
x² + x² + 12x + 36 - 144 = 0
2x² + 12x - 108 = 0
x² + 6x - 54 = 0
x² + 6x + 9 = 54 + 9 {completing the square}
(x + 3)² = 63
x + 3 = ±√63
x = 3 + √63 or x = 3 - √63
x = 10.92 or x = -4.92
Therefore, the radius x for the circle is derived to be 10.92 using the Pythagoras rule for the right triangle.
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1. Complete the table.
2. Write an addition equation and draw a number line diagram for B. Include the starting elevation,
change, and final elevation in your diagram.
The completed table is shown below:
starting elevation (feet)
change (feet)
final elevation (feet)
A
+200
75 up
275
B
+200
75 down
125
C
+200
200 down
0
D
+200
+25
225
the additional equation for B is:
final elevation for B = +200 feet - 75 feet
c. The line diagram is attached below.
How do we calculate?We can use the formula, to write an addition equation for B
final elevation = starting elevation + change
final elevation for B = +200 feet - 75 feet
We simplify this equation as:
final elevation for B = +125 feet
We draw a number line diagram for B, we can start at +200 feet (the starting elevation) and then move 75 units down (since the elevation is decreasing by 75 feet).
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You received a score of 3.4 on your annual review. Merit increases are given out at .5% at a score of 2.6 and it goes up 1% every .4 points. What is the increase you can expect to receive?
You can expect to receive the increase of percentage that is 2.5%.
What do you mean by percentage?The term "percentage" in mathematics can refer to either numbers or ratios that are stated as fractions of 100. In most cases, they are indicated by "%" or "percent."In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100. A% is a number that has neither dimensions nor a defined unit of measurement.
Given,
You received a score of 3.4 on annual review. Merit increases are given out at .5% at a score of 2.6 and it goes up 1% every .4 points.
Score received in the beginning = 2.6
Increase in score as a percentage equals 0.5%
Score increases by 1% for every 0.4 points.
The following rise will occur at 2.6 + 0.4 = 3.0 points.
Increase in percentage: 0.5 + 1= 1.5%
Score = 3.0 + 0.4 = 3.4 points will be the following point increment.
Score increase as a percentage: 1.5 + 1 = 2.5%
You can expect to receive the increase 2.5%
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Write an equation of the line below.
to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below
[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{0}}} \implies \cfrac{ 2 }{ 6 } \implies \cfrac{ 1 }{ 3 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{ \cfrac{ 1 }{ 3 }}(x-\stackrel{x_1}{0})\implies {\Large \begin{array}{llll} y=\cfrac{ 1 }{ 3 }x+2 \end{array}}[/tex]
Is (2, 7) a solution to this system of equations? y = 3x + 1 y = 2x + 5 yes or no
Answer:
No
Step-by-step explanation:
(x,y)=(2,7) is the solution for y=3x+1, but not for y=2x+5, so (2,7) isn't the solution to the system of equations.
whats the answer. please tell me cause these ads are out of control
Answer:
Step-by-step explanation:
if your on computer jus press refresh when your by the answer, it will show u for a split sec
what is the answer to this question?
This is not true, so there is no point c in the interval [tex](1, 8)[/tex] that satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = x-3.[/tex]
What is the mean value theorem?To apply the Mean Value Theorem, we need to check that the function [tex]f(x) = x-3[/tex] satisfies the following conditions:
f(x) is continuous on the closed interval [1, 8].
f(x) is differentiable on the open interval (1, 8).
Condition 1 is satisfied because f(x) is a polynomial function, and all polynomial functions are continuous everywhere.
To check condition 2, we can take the derivative of f(x) to get:
f'(x) = 1
The derivative is a constant function, so it is defined and continuous on the entire interval (1, 8).
Therefore, we can apply the Mean Value Theorem, which states that there exists a point c in the open interval (1, 8) such that:
[tex]f'(c) = (f(8) - f(1))/(8 - 1)[/tex]
Plugging in the values, we get:
[tex]1 = (8-3)/(8-1)[/tex]
Simplifying, we get:
[tex]1 = 5/7[/tex]
Therefore, This is not true, so there is no point c in the interval (1, 8) that satisfies the conclusion of the Mean Value Theorem for f(x) = x-3.
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Archaeology: Tree Rings. At Burnt Mesa Pueblo, the method of tree-ring dating gave the following years A.D. for an archaeological excavation site: 1189, 1271, 1267, 1272, 1268, 1316, 1275, 1317, 1275. Find a 90% confidence interval for the mean of all tree ring dates from this archeological site.
After answering the presented question, standard deviation t Lower bound = X - [tex](t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94[/tex]
What is standard deviation?A statistic that expresses the variability or variation of a bunch of values is the standard deviation. A high standard deviation indicates that the values are more distributed, whereas a low standard deviation indicates that the numbers are closer to the set mean. The standard deviation is a measure of how far the data are from the mean (or ). When the standard deviation is small, the data tends to cluster around the mean; when it is great, the data is more spread. The standard deviation represents the average variability of the data collection. It displays the average deviation from the mean of each score.
Next, we need to find the t-value for a 90% confidence interval with 8 degrees of freedom (n-1):
t = t(0.05, 8) = 1.860
Now we can calculate the lower and upper bounds of the confidence interval:
Lower bound = X - [tex](t * (s/\sqrt(n))) = 1271.89 - (1.860 * (34.753/\sqrt(9))) = 1238.94[/tex]
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HELP PLEASE!!! WILL GIVE BRAINLIEST
A linear relationship is shown in the table.
Time (hours) 2 4 6 8
Distance (miles) 4 8 12 16
Is the linear relationship also proportional? Explain.
No, the constant of proportionality is 2.
Yes, the constant of proportionality is 2.
No, there is no constant of proportionality.
Yes, there is no constant of proportionality.
Answer:
Yes, the c.o.p. is 2.
Step-by-step explanation:
The question of proportionality is answered by directly dividing each y-value (distance) by its associated x-value (time). If ALL of the related pairs give the same quotients, the relationship is proportional and the common quotient is the constant of proportionality.
4/2=2
8/4=2
12/6=2
16/8=2
Help please
Condense to a single logarithm is possible
In(6x^9)-In(x^2)
The condensed expression in to a single logarithm is In(6x⁷).
What is the condensed expression?Using the property of logarithms that states "the logarithm of the quotient is the difference of the logarithms", we can write:
In(6x⁹/x²)
Simplifying the expression within the parentheses, we get:
In(6x⁷)
Therefore, the condensed expression is In(6x⁷).
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An apple falls off a tree from a height of $36$36 feet.
a. What does the function $h(t)=-16t^2+36$h(t)=−16t2+36 represent in this situation?
BoldItalicUnderlineBullet listNumbered listSuperscriptSubscriptTable
0 / 10000 Word Limit0 words written of 10000 allowed
Question 2
b. Find and interpret the domain of h$h$h in this situation.
BoldItalicUnderlineBullet listNumbered listClear formattingSuperscriptSubscript
a)The term 1-16t²represents the effect of gravity on the apple, which causes it to fall with increasing speed. The constant term 36 represents the initial height of the apple
b)Interpreting the domain, we can say that h(t) makes sense only for non-negative values of t. In other words, we can use the function h(t)to find the height of the apple at any time t a
what is gravity ?
Gravity is a fundamental force of nature that causes objects with mass to attract each other. It is the force that keeps planets in orbit around stars, and stars in orbit around the center of their galaxies.
In the given question,
a. The function h(t)=-16t²+36 represents the height of an apple above the ground at time t after falling off a tree. The term1 -16t² represents the effect of gravity on the apple, which causes it to fall with increasing speed. The constant term 36 represents the initial height of the apple when it fell off the tree.
b. The domain of h(t) in this situation is the set of all possible values of t that make sense in the context of the problem. Since h(t) represents the height of the apple at time t after it fell off the tree, the domain of h(t)is the set of all non-negative real numbers, or [0,\infty) This is because time cannot be negative, and the apple cannot fall for an infinite amount of time.
Interpreting the domain, we can say that h(t)makes sense only for non-negative values of t. In other words, we can use the function h(t) to find the height of the apple at any time t after it fell off the tree, as long as t is non-negative..
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What is the value of -5n -23 when n=11?
Answer:
Step-by-step explanation:
Answer: -78
-5(11)-23=?
-55-23= -78
Answer:
-78
Step-by-step explanation:
n = 11
Replace n with its given value in this expression:
[tex] - 5n - 23[/tex]
[tex] - 5 \times 11 - 23 = - 55 - 23 = - 78[/tex]
Complete the following proof. Show all of your work.
Prove: The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
1. Assign (x,y) values to points A, B, and C.
2. Calculate the (x,y) values for point M.
3. Calculate the length of MA, MB, and MC. (Hint: use the distance formula.)
4. Given the three lengths, what can you conclude?
We have demonstrated that the middle of a right triangle's hypotenuse is equally spaced from its three vertices, MA = MB = MC.
Let A be the vertex of the right angle, B and C be the other two vertices, and let their (x,y) coordinates be as follows:
A: (a,b)
B: (c,d)
C: (e,f)
The midpoint M of the hypotenuse BC can be found by averaging the (x,y) coordinates of B and C:
[tex]M: $\left(\frac{c+e}{2},\frac{d+f}{2}\right)$[/tex]
To calculate the lengths of MA, MB, and MC, we can use the distance formula:
[tex]MA = \sqrt{(a - \frac{c+e}{2})^2 + (b - \frac{d+f}{2})^2}$\\$MB = \sqrt{(c - \frac{c+e}{2})^2 + (d - \frac{d+f}{2})^2}\\$MC = \sqrt{(e - \frac{c+e}{2})^2 + (f - \frac{d+f}{2})^2}$[/tex]
Simplifying each of these equations, we get:
[tex]MA = \sqrt{(2a - c - e)^2 + (2b - d - f)^2}/2$\\$MB = \sqrt{(c - e)^2 + (d - f)^2}/2$\\$MC = \sqrt{(2e - c - e)^2 + (2f - d - f)^2}/2$[/tex]
We want to show that the midpoint M of the hypotenuse BC is equidistant from the three vertices, i.e., that MA = MB = MC.
Substituting the coordinates of M into the expressions for MA, MB, and MC, we get:
[tex]$MA = \sqrt{(2a - c - e)^2 + (2b - d - f)^2}/2$$MB = \sqrt{(c - e)^2 + (d - f)^2}/2$$MC = \sqrt{(2e - c - e)^2 + (2f - d - f)^2}/2$[/tex]
To simplify these expressions, notice that[tex]$(c+e)/2$[/tex] is the x-coordinate of M, which is halfway between the x-coordinates of B and C. Similarly, [tex]$(d+f)/2$[/tex] is the y-coordinate of M, which is halfway between the y-coordinates of B and C. Therefore, we can rewrite the expressions as:
[tex]MA = \sqrt{(a - \frac{c+e}{2})^2 + (b - \frac{d+f}{2})^2}\\MB = \sqrt{(c - \frac{c+e}{2})^2 + (d - \frac{d+f}{2})^2}\\MC = \sqrt{(e - \frac{c+e}{2})^2 + (f - \frac{d+f}{2})^2}[/tex]
Notice that these are the same expressions we obtained in step 3 for the lengths of the three segments.
Therefore, we have shown that MA = MB = MC, which means that the midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
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Here is a Venn diagram showing the sets C and D, as well as the universal set U.
(The numbers shown are elements of these sets.)
(a) D' =
(b) CUD=
(c) CND' =
Find the sets below. Write each answer in roster form or as Ø.
The elements of the sets are;
'D = { 4, 6 , 8}
C∪D = { 2, 3, 5, 7}
C∩'D = { }
What is a Venn diagram?A Venn diagram is defined as a widely used diagram style showing the logical relation between sets.
The different sets in a Venn diagram are determined with the symbols;
∪ is used to determine the union of sets in which there is a combination of two or more sets without repetition of the elements.∩ is used to determine the intersection of sets in which the sets are sort for their common elements.From the Venn diagram shown, we have that;
Universal set = {4, 6, 8}
C = { 7}
D = { 2, 3 , 5}
Then, we have that;
'D = { 4, 6 , 8}
C∪D = { 2, 3, 5, 7}
C∩'D = { }
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Given the circle below with chords GH and IJ. Find the length of HK. Round to the nearest tenth if necessary. G 20 K 6 I 26 H J
The calculated value of the length of the segment HK is 7.8 units
Finding the length of the segment HKGiven the circle
And the intersecting chords IJ and GH
When two chords cross each other inside a circle, the product of the lengths of their respective line segments are equal.
In this particular circle, chords IJ and GH intersect at a point called K.
As a result, the product of the length of segments IK and KJ is equal to the product of the length of segments GK and HK.
So, we have
IK * KJ = GK * HK
This gives
6 * 26 = 20 * HK
This gives
HK = 7.8
Hence, the segment HK is 7.8 units long
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find the measure of minor arc RV
The measure of the minor arc m∡rv = 111°
What is the explanation for the above response?Recall that according to the principle of angle of intersecting secants, (a-b)/2 = c
Where a = ∡RV
b = ∡SU = 37°:
and c = ∠T (the angle between intersecting secants.
Thus, if (a-b)/2 = c, and b = c = 37 degrees, then we can substitute these values into the equation to get:
(a - 37) / 2 = 37
Multiplying both sides by 2 gives:
a - 37 = 74
Adding 37 to both sides gives:
a = 111
Therefore, a is equal to m∡rv = 111°.
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Consider the line =−8x7y−8.
Find the equation of the line that is parallel to this line and passes through the point −6, 4.
Find the equation of the line that is perpendicular to this line and passes through the point −6, 4.
Consequently, the equation of the line passing through (-6, 4) and perpendicular to the provided line is y = (7/8)x + 25/4.
How to calculate the equation of the line?We use the fact that parallel lines have the same slope to determine the equation of a line that is perpendicular to a given line and passes through a point. provided that it takes the form y = mx + b, where m is the slope, the provided line has a slope of -8/7. The parallel line will therefore similarly have a slope of -8/7.
The point-slope form of a line is used to determine the y-intercept of a parallel line: y - y1 = m(x - x1), where (x1, y1) is the point the line passes through. We obtain: y - 4 = (-8/7)(x + 6) by substituting (-6, 4) and -8/7 for m.
This equation can be simplified to y = (-8/7)x - 40/7.
We make use of the fact that perpendicular lines have opposing reciprocal slopes to determine the equation of a line that is perpendicular to the supplied line and passes through (-6, 4). provided that the provided line has a slope of -8/7, the perpendicular line will have a slope of 7/8.
Again using the point-slope representation of a line, we arrive at: y - 4 = (7/8)(x + 6)
This equation can be simplified to: y = (7/8)x + 25/4
Consequently, the equation of the line passing through (-6, 4) and perpendicular to the provided line is y = (7/8)x + 25/4.
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Of the following options, what could be a possible first step in solving the equation −7x − 5 = x + 3? (6 points) Group of answer choices Adding 7x to both sides of the equation Subtracting 5 from both sides of the equation Adding x to both sides of the equation Combining like terms, −7x + x = − 6x
Therefore, the solution of the given problem of equation comes out to be adding 7x to both sides of the equation might be the initial step towards solving the equation 7x 5 = x + 3.
What is equation?Variable words are often employed in complex algorithms to show consistency between two contradictory statements. Academic expressions called equations are used to show the equality of various academic figures. Think of the specifics with y + 7 proposals. In this situation, elevating results in b + 7 when building y + 7 is combined, in contrast to another method of splitting 12 equally sized pieces into two halves.
Here,
We can start by reducing the equation by using various algebraic operations in order to find the solution to the equation 7x 5 = x + 3.
The variable term on the right side of the equation would be eliminated, and the variable on the left side would be isolated, by adding 7x to both sides of the equation as a possible initial step:
=> -7x - 5 + 7x = x + 3 + 7x
Combining similar terms to make the left side simpler:
=> -5 = 8x + 3
After that, we may take 3 off of both sides:
=> -5 - 3 = 8x + 3 - 3
Making the right side simpler:
=> -8 = 8x
By multiplying both sides by 8, we may finally find the value of x:
=> x = -1
As a result, adding 7x to both sides of the equation might be the initial step towards solving the equation 7x + 5 = x + 3.
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Solve 2(5x + 9) = 6x+ 26.
A. x = -2
B. x= 11
C. x= -11
D. x = 2
how many tenths are equivalent to 13.2
Answer:132 tenths are equivalent to 13.2.
Step-by-step explanation:
Answer: 132 tenths.
Step-by-step explanation:
Since it's tenths, all you have to do is move the decimal place over 1 space.
Suppose you borrow $40,000 at 13% (.13) APR for a 12-year term to be paid monthly.
Your monthly payment is $450.00. How much of your first payment goes toward
interest?
Interest allocation formula if needed:
pays in a year
x principal = interest
Answer:
The interest portion of the first payment is $433.20.
Step-by-step explanation:
To find out how much of your first payment will go to interest, we need to calculate the monthly interest rate and then use it to calculate the interest portion of the monthly payment.
First, we need to calculate the monthly interest rate by dividing the annual interest rate by 12.
Annual interest rate = 13%
Monthly interest rate = 13%/12 = 0.01083
Next, we can use the monthly payment amount and the monthly interest rate to calculate the interest portion of the payment:
Interest portion of payment = Monthly interest rate x Remaining loan balance
To calculate the remaining loan balance after the first payment, we can use the formula for the present value of an ordinary annuity:
Remaining loan balance = Present value of remaining payments
Present value of remaining payments = Monthly payment x (1 - (1 + monthly interest rate)^-n) / monthly interest rate
where n is the total number of payments over the term of the loan.
n = 12 years x 12 months/year = 144 payments
Present value of remaining payments = $450 x (1 - (1 + 0.01083)^-144) / 0.01083 = $44,373.68
Remaining loan balance after first payment = $44,373.68 - $40,000 = $4,373.68
Finally, we can calculate the interest portion of the first payment:
Interest portion of payment = 0.01083 x $40,000 = $433.20
Therefore, the interest portion of the first payment is $433.20.
NEED help on questions 11-14 Please and Thank you
Answer:
11. (D) 90 degrees
12. (C) 93
13. (D) 90 degrees
14. (C) 46
Step-by-step explanation:
11. this is a square so each angle is 90 degrees.
12. as each side is the same, we create the equation 9x + 3 = 11x - 17. Solve.
13. With diagonals, MGQ, QGE, QEO, QOM, QMG become 45 degrees, while the intersection of the diagonals become 90 degrees
Hope this answers your question
please give Brainliest, would really appreciate it! :)
Can someone help me please?
Answer:
1.52
Step-by-step explanation:
divide 152 by 100
What is the value of P(X= 2 or X = 0)?
Enter your answer in the box.
P(X= 2 or X = 0) =
X
0
1
2
3
4
5
P
0.3
0.05
0.1
0.15
0.15
0.25
So, the value of P (X=2 or X=0) is 0.4.
What does probability mean?Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, with 0 indicating that an event is impossible, and 1 indicating that it is certain to occur.
For example, if you flip a fair coin, the probability of it landing on heads is 0.5 or 50%, as there are only two possible outcomes (heads or tails) and they are equally likely to occur.
Probability is used extensively in fields such as statistics, mathematics, and science to model and analyze uncertainty and randomness. It is also used in practical applications such as gambling, risk assessment, and decision making.
o find the probability of X being 2 or 0, we need to add the probabilities of the two events.
P(X=2 or X=0) = P(X=2) + P(X=0)
From the given table, we can see that:
P(X=2) = 0.1
P(X=0) = 0.3
Therefore,
[tex]P (X=2 or X=0) = 0.1 + 0.3 = 0.4[/tex]
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