Answer:
A quadratic function can have up to two x-intercepts.
An x-intercept of a quadratic function is also called a zero of the function.
Step-by-step explanation:
None needed.
The true statement is
An x-intercept of a quadratic function is also called a zero of the function.
A quadratic function can have up to two x-intercepts.
What is a quadratic function?A quadratic polynomial function has one or more variables and a variable with a maximum exponent of two. It is also known as the polynomial of degree 2 because the second-degree component in a quadratic function is the biggest degree term. A quadratic function must contain at least one term of the second degree. It possesses algebraic qualities.
we have,
The x-intercepts of quadratic functions,
The standard form of quadratic equation is
ax² + bx + c = 0
The zeroes of the quadratic functions are the values of x, which is also known as the x-intercept.
Because the degree of the polynomial is 2, there will be at least two x-intercept values.
The x-intercept is the x position at which the value of y is zero.
Let x = a be an x-intercept, and the function factor is (x - a).
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A gardener is planting two types of trees: Type A is 8 feet tall and grows at a rate of 7 inches per year. Type B is 2 feet tall and grows at a rate of 13 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.
Answer:
1 year
Step-by-step explanation:
8 + 7x = 2 + 13x
Move the 2 to the other side by subtracting 2 from both sides.
6 + 7x = 13x
Move the 7x to the other side by subtracting both sides by 7x.
6 = 6x
Divide both sides by 6.
1 = x
Therefore, x equals 1 and it will take 1 year for both trees to reach the same height.
The scores on a test are normally distributed with a mean of 150 and a standard deviation of 30. What is the score that is 1 standard deviation below the mean?
A score of 120 is one standard deviation below the mean of 150 on a test with a standard deviation of 30.
Explanation:The score that is 1 standard deviation below the mean is found by subtracting the standard deviation from the mean. In the context of this normal distribution of test scores, with a mean of 150 and a standard deviation of 30, we calculate the score one standard deviation below the mean as follows:
Score = Mean – Standard Deviation = 150 – 30 = 120
This calculation indicates that a score of 120 is one standard deviation below the mean on this test.
Which of the following has a constant of proportionality of 2?
A) y = 2 x
B) 2 y = x
C) y = x + 2
D) y + 2 = 2 x
Answer:
A) y = 2 x
Step-by-step explanation:
The equation for direct variation is
y = kx where the constant of proportionality is k
y = 2x
Sherry is cooking chicken for her family. She wants to be sure the chicken has an internal temperature of at least 170 degrees Fahrenheit. She uses a thermometer to measure the internal temperature at four randomly chosen places. The minimum reading in the sample is 180 degrees Fahrenheit. Identify the population, the parameter, the sample, and the statistic. Population, minimum temperature of 170 degrees Fahrenheit; parameter, all chicken meat temperature readings; sample, four random thermometer readings; statistic, minimum sample reading of 180 degrees Fahrenheit Population, all chicken meat temperature readings parameter, minimum temperature of 170 degrees Fahrenheit; sample, minimum sample reading of 180 degrees Fahrenheit; statistic, four random thermometer readings Population, four random thermometer readings; parameter, all chicken meat temperature readings; sample, minimum temperature of 170 degrees Fahrenheit; statistic, minimum sample reading of 180 degrees Fahrenheit Population, all chicken meat temperature readings; parameter, minimum temperature of 170 degrees Fahrenheit; sample, four random thermometer readings; statistic, minimum sample reading of 180 degrees Fahrenheit Population, minimum sample reading of 180 degrees Fahrenheit; parameter, all chicken meat; sample, minimum temperature of 170 degrees Fahrenheit; statistic, four random thermometer readings
Answer:
Population, all chicken meat; parameter, minimum temperature of 170 degrees Fahrenheit; sample, four random thermometer readings; statistic, minimum sample reading of 180 degrees Fahrenheit
Step-by-step explanation:
On Monday, 288 students went on a trip to the zoo. All 7 buses were filled and 8 students had to travel in cars. How many students were in each bus?
Answer:
40 kids
Step-by-step explanation:
288 minus the 8 kids that had to hide in cars= 280. 280 divided by the seven busses is 40
Help whats 2+2 please i cant figure it out its baby two right
2 + 2 =4 is four tgvjixyi9
Answer:
It’s 4 or fish
Step-by-step explanation:
According to the National Institute on Drug Abuse, a U.S. government agency, 17.3% of 8th graders in 2010 had used marijuana at some point in their lives. A school official hopes to show the percentage is lower in his district, testing LaTeX: H_0H 0: LaTeX: p=0.173p = 0.173 versus LaTeX: H_aH a: LaTeX: p<0.173p < 0.173. The health department for the district uses anonymous random sampling and finds that 10% of 80 eighth-graders surveyed had used marijuana. Are conditions met for use of the normal model to represent the distribution of sample proportions?
Answer:
The conditions for use of the normal model to represent the distribution of sample proportion are not met. He should increase the sample size until the conditions are met.
If the test is done anyway, the null hypothesis failed to be rejected.
The conclusion is taht there is not enough evidence to support the claim that the percentage is lower in this district.
Step-by-step explanation:
The conditions for use of the normal model to represent the distribution of sample proportion are not met, as the affirmative responses are less than 10.
[tex]np=80*0.1=8<10[/tex]
If the test of hypothesis is done as if the conditiones were met, we know that the claim is that the percentage is lower in this district.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.173\\\\H_a:\pi<0.173[/tex]
The significance level is 0.05.
The sample has a size n=80.
The sample proportion is p=0.1.
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.173*0.827}{80}}\\\\\\ \sigma_p=\sqrt{0.001788}=0.042[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.1-0.173+0.5/80}{0.042}=\dfrac{-0.067}{0.042}=-1.578[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-1.578)=0.057[/tex]
As the P-value (0.057) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the percentage is lower in this district.
When dragons on planet Pern lay eggs, the eggs are either green or yellow. The biologists have observed over the years that 32% of the eggs are yellow, and the rest green. Next spring the lead scientist has permission to randomly select 45 of the dragon eggs to incubate. Consider all the possible samples of 45 dragon eggs. What is the usual number of yellow eggs in samples of 45 eggs
Answer:
The usual number of yellow eggs in samples of 45 eggs is 14.4.
Step-by-step explanation:
For each egg, there are only two possible outcomes. Either they are yellow, or they are not. The probability of an egg being yellow is independent of other eggs, so we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
32% of the eggs are yellow
This means that [tex]p = 0.32[/tex]
45 eggs
This means that [tex]n = 45[/tex]
What is the usual number of yellow eggs in samples of 45 eggs
[tex]E(X) = np = 45*0.32 = 14.4[/tex]
The usual number of yellow eggs in samples of 45 eggs is 14.4.
In a random sample of 45 dragon eggs on planet Pern, we would typically expect around 14 to 15 eggs to be yellow, based on the given probability of an egg being yellow (which is 32%).
Explanation:The subject of the question relates to probabilities in statistics. Here, we are given that the chance a dragon's egg on planet Pern is yellow is 32% or 0.32 in decimal form. We are then asked to predict the number of yellow eggs in a group of 45 eggs.
To solve this, we simply multiply the total number of eggs by the notation of the probability:
45 eggs * 0.32 = 14.4
However, you can't have 0.4 of an egg, so we have to round this number to 14 or 15 eggs. Therefore, in a random sample of 45 dragon eggs, we would typically expect around 14 to 15 of them to be yellow assuming that the probability remains constant.
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observe as seguintes situações e sua representação em linguagem matematica dois numeros x e y são tais 2x y=6 x-y=3
Answer:
We have two relations
2*x*y = 6 (2 times x times y is equal to six)
x - y = 3 ( the difference between x and y is trhe)
Where whe have two variables, x and y.
To solve this system, the first step is isolation one of the variables in one of the equations, let's isolate x in the second equation.
x - y = 3
x = 3 + y
now we can replace this in the other equation and then solve it for y.
2*x*y = 6
2*(3 + y)*y = 6
6y + 2y^2 = 6
now we have the quadratic equation:
2y^2 + 6y - 6 = 0
the solutions are:
[tex]y = \frac{-6 + -\sqrt{6^2 - 4*2*(-6)} }{2*2} = \frac{-6 +- 9.2}{4}[/tex]
the solutions are:
y = (-6 + 9,2)/4 = 0.8
y = (-6 - 9.2)/4 = -3.8
if y = 0.8, then:
x = 3 + y = 3.8
if y = -3.8
x = 3 + y = 3 - 3.8 = -0.8
so we have two possible solutions:
(-0.8, -3.8) and (3.8, 0.8)
The speed of pickup of ride sharing services like Uber and Lyft seems to have surpassed that of ambulance services. The mean response time of ambulances across the United States is 15.3 minutes with a standard deviation of 12.8 minutes. For ride sharing services, the mean pick-up time across the United States is 8 minutes with a standard deviation of 5.2 minutes. Based on these estimates, which of the following gives the standard deviation of the sampling distribution of the difference in the sample means for samples of 30 ambulance rides and 40 ride sharing rides (Ambulance – Ride Sharing)?
Answer:
The correct answer is (C).
Because the sample sizes are less than 10% of their respective population sizes, the standard deviation of the difference in sample means is approximately≈2.912 minutes.
Step-by-step explanation:
Answer:
Step-by-step explanation:
The correct answer is (C).
Because the sample sizes are less than 10% of their respective population sizes, the standard deviation of the difference in sample means is approximately \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} = \sqrt{\frac{12.8^2}{30}+\frac{5.2^2}{40}} \approx 2.912
n
1
s
1
2
+
n
2
s
2
2
=
30
12.8
2
+
40
5.2
2
≈2.912 minutes.
Area =
22ft for diameter
Here is your answer! uwu
P
Q
R
S
T
-10
-8
6
4
2
0
2
4
6
Find the midpoint of PS.
73 POINTS need help
A large mall is built in the shape of a square. At each corner of the mall stands a pillar which is topped by a pyramid-shaped section of red tin roof, as shown in the picture below.
The pyramid is a square pyramid, measuring 21.5 feet on each of its base edges. The height of each of the triangular lateral face is 13.4 feet. Use this information to answer the following questions.
What is the area of the roof? [Type your answer as a number. Do not round.]
blank square yards
Answer:
2304.8 ft^2
Step-by-step explanation:
The lateral area of one of the pyramid is 21.5 * 13.4 * 4/2 = 576.2
There are 4 of them, so we multiply that by 4 : 576.2 * 4 = 2304.8
Mrs. Braddock has a bag containing 6 lipsticks, 4 eye shadows, 6 eye liners, and 5 mascaras. She will randomly choose one item from the bag.What is the probability that she will pull NOT lipstick? p(NOT lipstick). Round percents to nearest whole number
Answer:
The probability that she will not pull lipstick is 71%.
Step-by-step explanation:
The probability of an event E is the ratio of the favorable number of outcomes to the total number of outcomes.
[tex]P(E)=\frac{n(E)}{N}[/tex]
Here,
n (E) = favorable number of outcomes
N = total number of outcomes
The contents in Mrs. Braddock's bag are:
Number of lipsticks = n (L) = 6
Number of eye shadows = n (S) = 4
Number of eye liners = n (E) = 6
Number of mascaras = n (M) = 5
Total number of items in the bag = N = 21
Consider that the probability of an event occurring is P. Then the probability of the given event not taking place is known as the complement of that event.
Complement of the given event is, 1 – P.
Compute the probability of selecting a lipstick as follows:
[tex]P(L)=\frac{n(L)}{N}\\\\=\frac{6}{21}\\\\=\frac{2}{7}[/tex]
Compute the probability of not selecting a lipstick as follows:
[tex]P(L^{c})=1-P(L)[/tex]
[tex]=1-\frac{2}{7}\\\\=\frac{7-2}{7}\\\\=\frac{5}{7}[/tex]
Convert this probability into percentage as follows:
[tex]\frac{5}{7}\times 100 = 71.4286\approx 71\%[/tex]
Thus, the probability that she will not pull lipstick is 71%.
The cost medium pizza with no toppings is $7.50. The cost of each topping is $0.50. a) what is the equation that represents this relation if C represents the cost of pizza and N represents the number of topping?
Answer:$7.50+$0.50xN or C+$0.50xN
Step-by-step explanation:
Because the pizza is 7.50 and the extra toppings are 0.50 cents so the number of toppings is n and the cost for the pizza is c so C+0.50xN.
Good Luck!!
What’s the correct answer for this?
Answer:
A
Step-by-step explanation:
Plate X will result in the lightest place since it's density and thickness both are less.
Awnser this please.
Answer:
1.5 hours
Step-by-step explanation:
make each half hour represent t
Cost C(t) = 24 + 14t
66 = 24 + 14t
42 = 14t
t = 3
3 half hours = 1.5 hours
Answer:
1 and a half hours of work
Step-by-step explanation:
You minus 66 and 24 to get 42. Then you divide 42 and 14
statistical analyst for the Wall Street Journal randomly selected six companies and recorded both the price per share of stock on January 1, 2009 and on April 30, 2009. The results are presented below. Suppose the analyst wished to see if the average price per share of stock on April 30, 2009 is greater than the average price per share of stock on January 1, 2009 at α=.025. Apr. 30, 2009 33 33 34 30 33 38 Jan. 1, 2009 21 25 30 33 23 27 For the hypothesis stated above, what is the P-value?
Answer:
p value= 2.228
Step-by-step explanation:
since average of two groups is being compared two-sample t-test will be performed.
degrees of freedom= 12-2=10
at α=.025 from t table
p value= 2.228
Suppose Kristen is researching failures in the restaurant business. In the city where she lives, the probability that an independent restaurant will fail in the first year is 32 % . She obtains a random sample of 72 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. What are the mean and standard deviation of the number of restaurants that failed within a year? Please give your answers precise to two decimal places.
Answer:
The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.
Step-by-step explanation:
For each restaurant, there are only two possible outcomes. Either it fails during the first year, or it does not. The probability of a restaurant failling during the first year is independent of other restaurants. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
The probability that an independent restaurant will fail in the first year is 32%.
This means that [tex]p = 0.32[/tex]
72 independent restaurants
This means that [tex]n = 72[/tex]
Mean:
[tex]E(X) = np = 72*0.32 = 23.04[/tex]
Standard deviation:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{72*0.32*0.68} = 3.96[/tex]
The mean of the number of restaurants that failed within a year is 23.04 and the standard deviation is 3.96.
Final answer:
The mean number of independent restaurants in the sample expected to fail within the first year is 23.04, and the standard deviation is approximately 4.28.
Explanation:
To find the mean and standard deviation of the number of restaurants that failed within a year in Kristen's research, we can use the properties of the binomial distribution. The probability of a single restaurant failing (success in this context) is 0.32 (32%). Given a sample size of 72 restaurants, the mean number of restaurants that fail within a year is the product of the sample size and the probability of failure.
The formula for the mean (μ) of a binomial distribution is μ = n * p, where n is the sample size and p is the probability of success. Therefore, the mean number of failed restaurants is 72 * 0.32 = 23.04.
The formula for the standard deviation (σ) of a binomial distribution is σ = √(n * p * (1 - p)). Thus, the standard deviation of failed restaurants is √(72 * 0.32 * (1 - 0.32)) = √(72 * 0.32 * 0.68) ≈ 4.28.
Therefore, the mean number of restaurants that failed within a year is 23.04, and the standard deviation is approximately 4.28.
Which represents a quadratic function?
f(x) = −8x3 − 16x2 − 4x
f (x) = three-quarters x 2 + 2x − 5
f(x) = StartFraction 4 Over x squared EndFraction minus StartFraction 2 Over x EndFraction + 1
f(x) = 0x2 − 9x + 7
Answer:[tex]f(x)=\frac{3}{4}x^2+2x-5[/tex]
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
b
1. Write an expression that represents the area of a rectangle given that the Length = (x+3) and the width = (3x + 4).
2. The area of a rectangle is 28x2 – 13xy – 6y2 square units. If the length of the rectangle is 7x + 2y units, then find the breadth of the rectangle, hence find the perimeter of the rectangle
Answer:
(7x+2y)- length (4x-3y)- width
22x-2y is the perimeter.
Step-by-step explanation:
A sociologist develops a test to measure attitudes towards public transportation, and 25 randomly selected subjects are given the test. The sample mean score is 76.2 and the sample standard deviation is 21.4. The population is normally distributed. What is the 95% confidence interval for the mean score of all such subjects? Round to 3 decimal places.
Final answer:
The 95% confidence interval for the true mean score of subjects' attitudes towards public transportation is between 67.361 and 85.039, computed using a t-score for a sample size of 25.
Explanation:
To calculate the 95% confidence interval for the mean score of all subjects regarding their attitudes towards public transportation, we will use the following formula for a confidence interval when the population is normally distributed but the population standard deviation is not known:
CI = ± t*(s/√n), where CI is the confidence interval, ± denotes plus or minus, t is the t-score that corresponds to the desired level of confidence and degrees of freedom (df = n - 1), s is the sample standard deviation, and √n is the square root of the sample size.
For our sample size of n = 25, the degrees of freedom is df = 24. Consulting a t-distribution table or using statistical software to find the t-value for df = 24 at a 95% confidence level, we assume a t-value approximately equal to 2.064 (this may slightly vary depending on the source of the t-distribution table). Plugging in the values:
CI = ± 2.064*(21.4/√25), thus the margin of error is approximately 2.064 * 4.28
The confidence interval is then the sample mean ± the margin of error:
76.2 ± (2.064 * 4.28)
This calculation yields a confidence interval for the population mean score of:
Lower Bound = 76.2 - 8.83872 ≈ 67.361
Upper Bound = 76.2 + 8.83872 ≈ 85.039
Therefore, rounding to three decimal places: 67.361 (Lower Bound) and 85.039 (Upper Bound).
We are 95% confident that the true mean score of all subjects' attitudes towards public transportation lies between 67.361 and 85.039.
What is the lateral surface area of the square pyramid below?
a
48 in²
b
105 in²
c
96 in²
d
57 in²
Answer:
lateral surface area = 48 inches²
Step-by-step explanation:
The picture below is the square base pyramid you are referring. The lateral area is adding the area of the 4 triangles in the pyramid.
area of a triangle = 1/2 × b × h
The slant height of the triangle is gotten using Pythagoras theorem
lateral surface area = 4 × (1/2 × 3 × 8)
lateral surface area = 4 × 24/2
lateral surface area = 4 × 12
lateral surface area = 48 inches²
Answer:
48 in
Step-by-step explanation:
<3 hoped this helped <3
Over the past few decades, public health officials have examined the link between weight concerns and teen girls' smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that less than thirty percent of the teen girls smoke to stay thin? g
Answer:
We conclude that less than thirty percent of the teen girls smoke to stay thin.
Step-by-step explanation:
We are given that the Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old).
After four years the girls were surveyed again. Sixty-three said they smoked to stay thin.
Let p = percentage of the teen girls who smoke to stay thin.
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\geq[/tex] 30% {means that at least thirty percent of the teen girls smoke to stay thin}
Alternate Hypothesis, [tex]H_A[/tex] : p < 30% {means that less than thirty percent of the teen girls smoke to stay thin}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample % of teen girls who smoke to stay thin = [tex]\frac{63}{273}[/tex] = 0.231
n = sample of teen girls = 273
So, test statistics = [tex]\frac{0.231-0.30}{\sqrt{\frac{0.231(1-0.231)}{273} } }[/tex]
= -2.705
The value of z test statistics is -2.705.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the z table gives critical value of -1.645 for left-tailed test.
Since our test statistics is less than the critical value of z as -2.705 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that less than thirty percent of the teen girls smoke to stay thin.
About 23% of the surveyed girls smoked to maintain or lose weight. Social and cultural factors contribute to this behavior, which often leads to health issues. Broader and more comprehensive studies are needed for a conclusive answer.
Explanation:Yes, there's some evidence to suggest fewer than thirty percent of teen girls smoked to stay thin. Only 63 girls out of the 273 surveyed stated they smoked for weight issues, which equates to around 23%. However, this result is not conclusive, as it is based solely on the girls who participated in this particular study. For a more comprehensive conclusion, we would need to evaluate multiple studies with larger participant samples.
In broader context, the challenges teens face with self-image are due in part to sociocultural factors, such as the beauty ideal of thinness often emphasized in media. The image of thin models contributes significantly to body image concerns and associated behaviours like smoking to maintain or lose weight. Such behaviours can lead to health problems including, but not limited to, type 2 diabetes, heart disease, and even cancer.
Also, obesity is a rising epidemic affecting many, with its highest rates found in the United States. Increasing awareness about these issues and promoting healthier methods of maintaining weight can help in addressing these problems.
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A brokerage charges ? regardless of whether an investor buys or sells assets, and ? are incurred with every transaction
Answer:
Yes, that's true.
Step-by-step explanation:
A brokerage fee is the commission paid to a salesperson or broker for selling insurance or securities, respectively. The amount of this fee is usually calculated as a percentage of the transaction price, though it may be a flat fee.
brokerage fee compensates a broker for executing a transaction. It is usually, but not always, a percentage of the transaction value. In finance, stockbrokers most often come to mind, but real estate agents and business brokers frequently charge brokerage fees
Answer:
A brokerage charges brokerage account fees regardless of whether an investor buys or sells assets, and trade commissions are incurred with every transaction.
The equation y= 2x represents a set of data.
Which statement is NOT true?
Answer:
2 is an initial value
tell me if its right because i garuntee it is
Find an equation of the circle that has center(-3,4) and passes through(1,-2)
Answer:
(x +3)^2 +(y -4)^2 = 52
Step-by-step explanation:
The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2
We are given the value of (h, k), and we can find the value of r^2. Using the values of h and k, our equation is ...
(x +3)^2 +(y -4)^2 = r^2
Since we know this equation is satisfied by the point (1, -2), we can use this point in the equation to find r^2:
(1 +3)^2 +(-2 -4)^2 = r^2
16 +36 = r^2 = 52
The equation of the circle is ...
(x +3)^2 +(y -4)^2 = 52
The minute hand on a clock is 9 centimeterslong and travels through an arc of 252° every 42 minutes. To the nearest tenth of a centimeter, how far does the minute handtravel during a 42-minute period?
Answer: the minute hand travel 39.6 cm
Step-by-step explanation:
Length of minute hand of a clock = 9 cm
Central angle made by the minute hand = 252°
To find: how far the minute hand travel
Therefore
Length of minute hand is equal to the radius of circle
As we know the circumference of a circle is given by
[tex]C= 2\pi r \dfrac{\theta}{360^\circ}[/tex] where C is circumference , r is radius and ∅ is the central angle
So we have
[tex]C= 2 \times \dfrac{22}{7} \times 9 \times \dfrac{252^\circ}{360^\circ} \\\\\Rightarrow C= 2 \times \dfrac{22}{7} \times \dfrac{252^\circ}{40^\circ} \\\\\Rightarrow C= \dfrac{11}{7} \times \dfrac{252^\circ}{10^\circ} = 39.6[/tex]
Hence, the minute hand travel 39.6 cm in 42 minute period
Final answer:
The minute hand of the clock, which measures 9 centimeters in radius, travels approximately 39.3 centimeters along the arc when it moves through a 252-degree central angle in a 42-minute period.
Explanation:
To determine how far the minute hand of a clock travels in a 42-minute period, we need to calculate the arc length, which is a portion of the circumference of the circle traced by the minute hand's tip. We are given that the minute hand is 9 centimeters long, meaning it is the radius of the circle, and it travels through an arc of 252° during a period of 42 minutes.
The formula to calculate the arc length is:
ℓ = θ/360 × 2πr
Where:
ℓ is the arc length
θ is the central angle in degrees
r is the radius of the circle
In this case:
θ = 252°
r = 9 cm
Now, let's substitute these values into the formula:
ℓ = 252/360 × 2 × π × 9
ℓ ≈ 0.7 × 2 × 3.14159 × 9
ℓ ≈ 39.27 cm
So, to the nearest tenth of a centimeter, the minute hand travels approximately 39.3 cm during a 42-minute period.
How many solutions does the equation 3(x + 2) – 10 = 4x – 6 + x have?
Answer:
1
Step-by-step explanation:
3(x+2)-10=4x-6+x
3x+6-10=5x-6
2x=2
x=1
This is the only solution to this equation, meaning that there is only one solution to the equation. Hope this helps!
The equation 3(x + 2) - 10 = 4x - 6 + x has one solution, which is x = 1. After simplifying the equation and solving for x, we confirm that substituting x = 1 back into the equation results in an identity, indicating that this is the correct solution.
To determine how many solutions the equation 3(x + 2) \\- 10 = 4x \\- 6 + x has, we must first simplify the equation and solve for x.
Let's simplify both sides of the equation:
Distribute the 3 on the left side: 3x + 6 \\- 10 = 4x \\- 6 + x.
Combine like terms on the right side: 3x \\- 4 = 5x \\- 6.
Get all the x terms on one side and constants on the other: 3x \\- 5x = \\-6 + 4.
Simplify the equation: \ -2x = \\-2.
Divide both sides by \\-2 to solve for x: x = 1.
So, the solution to the equation is x = 1. To verify that this is the solution, we can substitute x = 1 back into the original equation and check that it holds true, which would confirm that the equation is an identity. In this case, the substitution leads to an identity, confirming that x = 1 is the correct and only solution to the equation.
Which of the following is the equation of a direct variation that has a constant of variation equal to -1/2?
A. y= x- 1/2
B. -1/2 y=x
C. y= -2x
D. y= -1/2x
I think it is c. y= -2x hope you have a good day!