In the third step, 10 is the mass of the dog. As such, it should have been substituted to w and not to m.
Answer:
its c/third step
Step-by-step explanation:
trust -w-
An assortment of 200 pencils is sold through a catalog for $\$19.90$. Shipping is an additional $\$6.95$. Including the charges for both the pencils and the shipping, what is the average cost, in cents, for each pencil
Answer:
13.425¢ per pencil
Step-by-step explanation:
The per-pencil cost is the total cost divided by the number of pencils.
ApplicationThe total cost is the cost for 200 pencils plus the cost for shipping:
total cost = $19.90 +6.95 = $26.85
The cost per pencil is ...
total cost / number of pencils = $26.85 / 200 = $0.13425 = 13.425¢
The average cost per pencil is 13.425 cents.
simplify
\( \sqrt{18} + \sqrt{50} - 2 \sqrt{8} \)
answer pls
Step-by-step explanation:
\(\sqrt{18} = 3\sqrt{2}\)
\(\sqrt{50}=5\sqrt{2}\)
\(2\sqrt{8} = 4\sqrt{2}\)
So \(3\sqrt{2} +5\sqrt{2} -4\sqrt{2}\)
= \(4\sqrt{2}\)
Please give me a brainliest answer
\(\frac{m}{2} =\frac{m+5}{10}\)
Answer:
\( \sf \large \: m=−1\)
Step-by-step explanation:
Let's solve your equation step-by-step.
m/2 =m+5/10
Step 1: Simplify both sides of the equation.
1/2m=m+1/2
Step 2: Subtract m from both sides.
1/2m−m=m+1/2−m
−1/2m=1/2
Step 3: Multiply both sides by 2/(-1).
(2/−1)*(−1/2m)=(2/−1)*(1/2)
m=−1
(a) what is the probability that a randomly selected woman has a diastolic blood pressure less than 60 mm hg?
Assuming normal distribution, we can calculate the probability of a woman having a diastolic blood pressure less than 60 mm Hg using a z-score and standard normal distribution table. The probability is approximately 0.04%.
The probability that a randomly selected woman has a diastolic blood pressure less than 60 mm Hg depends on the distribution of the diastolic blood pressure in the population.
Assuming that the diastolic blood pressure in women follows a normal distribution with mean µ and standard deviation σ, we can use the standard normal distribution to calculate the probability.
Let Z be the standard normal random variable, given by:
Z = (X - µ) / σ
where X is the diastolic blood pressure, µ is the mean diastolic blood pressure for women, and σ is the standard deviation of the diastolic blood pressure for women.
To find the probability that a randomly selected woman has a diastolic blood pressure less than 60 mm Hg, we need to calculate the corresponding z-score and then look up its probability in the standard normal distribution table.
The z-score can be calculated as:
Z = (60 - µ) / σ
Once we have the z-score, we can use a standard normal distribution table or software to find the probability. For example, using a table, we can find that the probability of a randomly selected woman having a diastolic blood pressure less than 60 mm Hg is approximately 0.0004, or 0.04%.
know more about standard normal distribution here: brainly.com/question/15103234
#SPJ11
the sum of a number times 8 and 24 is less than -21
Translate the sentence into an inequality
The inequality representing the given sentence is x < -45/8. This means that 'x' is a number less than -45/8.
Let's translate the given sentence into an inequality.
"The sum of a number times 8 and 24 is less than -21."
Let's represent the unknown number as 'x'. According to the sentence, the sum of 'x' multiplied by 8 and 24 is less than -21.
Mathematically, we can write this as:
8x + 24 < -21
This inequality states that when we multiply 'x' by 8, add 24 to the result, the sum is less than -21.
To solve this inequality for 'x', we can isolate 'x' on one side of the inequality sign:
8x < -21 - 24
Simplifying:
8x < -45
Finally, we divide both sides of the inequality by 8 (since it is a positive number):
x < -45/8.
For more such questions on Inequality:
https://brainly.com/question/25275758
#SPJ8
Are the equations 3x + 12 = 6 and -2 = 4 -3x equivalent? Explain
Answer:
The equations 3x + 12 = 6 and -2 = 4 -3x are not equivalent .
Step-by-step explanation:
3x + 12 = 6....i)
Firstly taking equation ...i) and solving for x
=> 3x = 6-12
=> 3x = -6
=> x = -6/3
=> x = -2
Then equation ...ii)
-2 = 4 -3x.....ii)
=> 3x = 4+2
=> 3x = 6
=> x = 6/3
=> x = 2
Hence , 2 ≠ -2
and the equations are not equivalent ..
Are the following functions analytic? Use (1) or (7). 2. f(z)=iz
z
ˉ
3. f(z)=e
−2x
(cos2y−isin2y) 4. f(z)=e
x
(cosy−isiny) 5. f(z)=Re(z
2
)−iIm(z
2
) 6. f(z)=1/(z−z
5
) 7. f(z)=i/z
8
8. f(z)=Arg2πz 9. f(z)=3π
2
/(z
3
+4π
2
z) 10. f(z)=ln∣z∣+iArgz 11. f(z)=cosxcoshy−isinxsinhy
The following functions are analytic:
1. f(z) = iz
2. f(z) = \(e^(^-^2^x^)(cos^2^y - isin^2^y^)\)
4. f(z) = \(e^x(cosy - isiny)\)
5. f(z) = \(Re(z^2) - iIm(z^2)\)
8. f(z) = \(i/z^8\)
11. f(z) = cos(x)cos(hy) - isin(x)sin(hy)
Analytic functions are those that can be expressed as power series expansions, meaning they have derivatives of all orders in their domain. In the given list of functions, we need to determine if each function satisfies this criterion.
f(z) = iz: This function is linear and can be expressed as a power series, therefore it is analytic.f(z) = \(e^(^-^2^x^)(cos^2^y - isin^2^y)\): This function can also be expressed as a power series expansion and has derivatives of all orders, making it an analytic function. f(z) = \(e^x(cosy - isiny)\): Similarly, this function can be written as a power series expansion and has derivatives of all orders, making it analytic. f(z) = \(Re(z^2) - iIm(z^2)\): Although this function involves the real and imaginary parts of \(z^2\), both of these components can be expressed as power series expansions, implying that f(z) itself can be written as a power series and is thus analytic.f(z) = \(i/z^8\): This function can be rewritten as i*\((1/z^8)\) , where \(1/z^8\) can be expressed as a power series expansion. Since the multiplication of a constant (i) and an analytic function (\(1/z^8\)) results in an analytic function, f(z) is analytic. f(z) = cos(x)cos(hy) - isin(x)sin(hy): This function consists of the multiplication and addition of trigonometric functions, which are themselves analytic. Therefore, f(z) is an analytic function.Learn more about Analytic functions
brainly.com/question/34499160
#SPJ11
researchers randomly assign study participants to one of two groups: the experimental group receives the and the control group receives the .
This is Single-Blinded Randomized Controlled trial type of study because the recipient is unaware that they are receiving a treatment, only the researchers are aware of who is receiving which treatment. So the option d is correct.
One of the most rigorous research designs is experimental research, which is frequently referred to as the "gold standard" in research designs.
This design involves the researcher manipulating one or more independent variables (as treatments), randomly assigning individuals to various treatment levels (random assignment), and observing the effects of the treatments on outcomes (dependent variables).
Experimental research has a distinct advantage in that it may link cause and effect through treatment manipulation while controlling for the erroneous effect of unrelated variables, which is known as internal validity (causality).
To learn more about Single-Blinded Randomized Controlled link is here
brainly.com/question/9292513
#SPJ4
The complete question is:
A team of researchers randomly separates their study's participants into two groups, giving one group a placebo and the other a new treatment to be tested. As the treatment is somewhat experimental, participants do not know whether they receive the placebo but researchers do know whether a specific participant receives the placebo. What type of study is this?
a. Standard Deviation Study
b. Type 1 Study
c. Case-Control Study
d. Non-Blinded Randomized Controlled Trial
e. Single-Blinded Randomized Controlled trial
Lots of points
For the line segment whose endpoints are L (0, 1) and M (2, 8), find the y coordinate for the point located 3 over 5 the distance from L to M.
5. 2
3. 5
4. 8
1. 6
The y-coordinate for the point located 3/5 the distance from L to M is 6.
A line segment is a part of a line that extends between two endpoints. The length of a line segment can be calculated by determining the difference between the coordinates of the endpoints of the line segment, both horizontally (the x-coordinates) and vertically (the y-coordinates).
Using these information, we will find the coordinates of a point which is 3/5 of the distance from L to M.
The distance between L(0,1) and M(2,8) is calculated as follows:
d(L, M) = √[(8 - 1)² + (2 - 0)²] = √65.
To determine the x-coordinate of the point 3/5 of the way from L to M, we can use the formula:
x = x₁ + (3/5)(x₂ - x₁) = 0 + (3/5)(2 - 0) = 1.2
To determine the y-coordinate of the point, we can use the formula:
y = y₁ + (3/5)(y₂ - y₁) = 1 + (3/5)(8 - 1) = 6
Therefore, the y-coordinate of the point 3/5 of the way from L to M is 6.
Learn more about line segment from the given link
https://brainly.com/question/280216
#SPJ11
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If b=2.2 yards and c=8 yards, what is the perimeter? If necessary, round to the nearest tenth.
PLEASEEE HURRYYY AND VERIFY YOUR ANSWER
Write an equation of the line in point-slope form that passes through the given points in the table. Then write the equation in slope-intercept form.
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.
\((\stackrel{x_1}{-16}~,~\stackrel{y_1}{-69})\qquad (\stackrel{x_2}{8}~,~\stackrel{y_2}{-33}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-33}-\stackrel{y1}{(-69)}}}{\underset{\textit{\large run}} {\underset{x_2}{8}-\underset{x_1}{(-16)}}} \implies \cfrac{-33 +69}{8 +16} \implies \cfrac{ 36 }{ 24 } \implies \cfrac{ 3 }{ 2 }\)
\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-69)}=\stackrel{m}{ \cfrac{ 3 }{ 2 }}(x-\stackrel{x_1}{(-16)}) \\\\\\ y +69 = \cfrac{ 3 }{ 2 } ( x +16)\implies y+69=\cfrac{ 3 }{ 2 }x+24\implies {\Large \begin{array}{llll} y=\cfrac{ 3 }{ 2 }x-45 \end{array}}\)
In what proportion should a 20% cream be mixed with a 5% cream of the same active ingredient to make a 10% cream? Write your answer in X:Y format.
Proportion should a 20% cream be mixed with a 5% cream of the same active ingredient to make a 10% cream the proportion in which the 20% cream should be mixed with the 5% cream to make a 10% cream is X:Y = 1:2.
To determine the proportion in which a 20% cream should be mixed with a 5% cream to make a 10% cream, we can once again use the concept of weighted averages.
Let's assume we mix X parts of the 20% cream with Y parts of the 5% cream.
The equation for the weighted average can be written as:
(Percentage A * Weight A) + (Percentage B * Weight B) = Desired Percentage * Total Weight
In this case, the equation would be:
(20% * X) + (5% * Y) = 10% * (X + Y)
Simplifying the equation, we get:
0.2X + 0.05Y = 0.1X + 0.1Y
Rearranging the terms, we have:
0.1X = 0.05Y
Dividing both sides by 0.05Y, we get:
(0.1X) / (0.05Y) = 1
Simplifying further:
2X = Y
Therefore, the proportion in which the 20% cream should be mixed with the 5% cream to make a 10% cream is X:Y = 1:2.
To know more about proportion refer here:
https://brainly.com/question/33460130#
#SPJ11
1. The sum of a number and six less than twice that number is twelve. Write an equation that can be used to
find that number, n. You do not need to solve. **
Answer: n + 2n - 6 = 12
Step-by-step explanation:
The number is n.
Six less than twice the number can be expressed as = 2n - 6
Adding those together will be; n + 2n - 6
They add up to 12 so the equation is;
n + 2n - 6 = 12
You said I don't need to solve but the number is 6 just in case.
What is the area of the pentagon, rounded to the nearest tenth?
13.8 cm2
17.3 cm2
32.7 cm2
69.0 cm2
The area of the pentagon, rounded to the nearest tenth will be 32.7 square cm. Then the correct option is C.
What is a polygon?The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.
A regular pentagon has an apothem measuring 3 cm and a perimeter of 21.8 cm.
Then the side length of the pentagon will be
5 x Side length = 21.8 cm
Side length = 4.36 cm
Then the area of the pentagon, rounded to the nearest tenth will be
Area of pentagon = 5 x area of triangle
Area of pentagon = 5 x 1/2 x 4.36 x 3
Area of pentagon = 32.7 square cm
Thus, the correct option is C.
More about the polygon link is given below.
https://brainly.com/question/17756657
#SPJ1
multiple choice question:
simplify √-72 .
A) -6√2
B) 3√-2
C) 3√2i
D) 3i√2
Answer:
im really not to sure on this one. sorry dude
Step-by-step explanation:
Use a graphing calculator to solve the system of linear equations
y=6x-11
-2x-3y=-7
Answer:
( 2, 1 )
Step-by-step explanation:
- 2x - 3y = - 7
- 3y = 2x - 7
y = - \(\frac{2}{3}\) x + \(\frac{7}{3}\)
( - 1, 3 ), ( 5, - 1 )
In a sale, the selling price of a bicycle is reduced by 20%. Find the sale price of the bicycle, given that its normal selling price is Rs 3300.
Answer:
1-0.2=0.8
0.8*3300= 2640
Original price = 3300
sale = 20% = 3300×20/100 = 660
Selling price= 3300-660= 2640 rs
the sale price of the bicycle is 2640 Rs
What are the coefficients in the equation?
–2x+4=15x
Answer:
\({ \rm{ - 2x + 4 = 15x}}\)
-2 & 15
Coefficients (in -2x+4=15x):
-2415What are coefficients?
Coefficients are the constants in an equation.
im finna ask a question
A circle is drawn with a center point of q. janelle wishes to construct a tangent to the circle that passes through point b. she starts by connecting points q and b to form line segment bq.
what is the best next step when constructing a tangent to the circle?
a
strike an arc on bq with a center of b that has a length the same as the radius of circle q.
b
draw a line straight down from point q to the bottom of the circle.
c
extend bq through the other side of the circle.
d
find the midpoint of bq.
The best step when constructing a tangent to the circle is to strike an arc on bq with a center of b that has a length the same as the radius of circle q. The correct answer is option a.
When constructing a tangent to a circle with a center point of Q that passes through point B, and having already connected points Q and B to form line segment BQ, the best next step is to: A) Strike an arc on BQ with a center of B that has a length the same as the radius of circle Q.
This will help you find the point where the tangent line intersects the circle, allowing you to complete the tangent construction. The tangent line will be perpendicular to the radius at the point of tangency.
Therefore option a is correct.
Learn more about Tangent:
https://brainly.com/question/30162650
#SPJ11
3. Mary is a real estate agent. One month she sold 7 houses at these prices: $171 000, $165 000, $178 000, $161 000, $174 000, $168 000, $240 000
3.a) What is the median price of the houses she sold?
3.b) Do you think the mean price is greater than or less than the median price of the houses sold that month? Why?
3.c) Which average do you think better represents a typical price of houses she sold that month? Why?
The median price of the houses sold will be equal to $171000 and yes, the mean price is greater than the median price of the houses.
What is Mean?Mean in mathematics is a quantity that falls somewhere between the extremes of a set. There are different types of meanings, and how they are calculated relies on the connection that is known about or is believed to control the other members.
a.
The median of given prices will be,
Let's arrange the given prices in ascending order,
161000, $165000, $168000, $171000, $174000, $178000, $240000
Then, the middle term is the median,
So, median = $171000
b.
Number of terms = 7
The mean of the given prices will be,
(171000 + 165000 + 178000 + 161000 + 174000 + 168000 +240000)/7
= 1257000/7
Mean = 179571.4286
Comparing mean and median, the mean price is greater than the median.
To know more about Mean:
https://brainly.com/question/23263573
#SPJ1
a digital scale measures weight to the nearest 0.2 pound which measurement shows an apporpriate level of precision for the scalae brainly
A. 130.4 pounds shows an appropriate level of precision for the scale
The quantity 0.2 pound represents readability of the digital scale. It is also known by the terms division size or resolution. The number indicates the division in digital scale. The scale division will be 20 in case 0.2 readability. Another example of readability can be understood by more simple divisions. For instance, 1 gram readability can be divided into divisions like 5 or 25 etc.
Capacity, is another term related to digital scale. It refers to the highest amount that can be weighed safely by the digital scale. Precision is defined as the total number of digits in any given number. Among the given options, the option with 4 digits will be the correct option. This is represented in option A. 130.4 pounds. Hence, it shows an appropriate level of precision.
The complete question is -
A digital scale measures weight to the nearest 0.2 pound. Which
measurement shows an appropriate level of precision for the scale?
A.130.4 pounds
B.124.75 pounds
C.125 pounds
D.120 pounds
Learn more about precise measurement on scale -
https://brainly.com/question/14654372
https://brainly.com/question/3019683
#SPJ4
What is x?
3/6=5.5/x
Answer:
x = 11
Step-by-step explanation:
3/6=5.5/x
Cross multiply.
3 * x = 6 * 5.5
x = 2 * 5.5
x = 11
Peter guesses on all 10 questions of a multiple-choice quiz. Each question has 4 answer choices, and Peter needs to get at least 7 questions correct to pass. Here are some probabilities computed using the binomial formula: P(getting exactly 7 correct) = 0.0031 P(getting exactly 8 correct) = 0.000386 P(getting exactly 9 correct) = 2.86 × 10−5 P(getting exactly 10 correct) = 9.54 × 10−7. Using the information, combine the individual probabilities to compute the probability that Peter will pass the quiz.
a. 0.001
b. 0.002
c. 0.0035
d. 0.005
Using the information, combine the individual probabilities to compute the probability that Peter will pass the quiz is (c) 0.0035.
Probability of Peter Passing QuizTo compute the probability that Peter will pass the quiz (i.e., get at least 7 questions correct), we need to sum the probabilities of getting exactly 7, exactly 8, exactly 9, and exactly 10 questions correct.
So, the probability of passing the quiz is:
P (getting at least 7 correct) = P (getting exactly 7 correct) + P (getting exactly 8 correct) + P (getting exactly 9 correct) + P (getting exactly 10 correct)
= 0.0031 + 0.000386 + 2.86 × 10⁻⁵ + 9.54 × 10⁻⁷
= 0.0035
Therefore, the result is c. 0.0035.
The binomial formula can be used to solve a wide range of problems in probability and statistics. The binomial formula is used to calculate the probability of getting a specific number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure).
Learn more about Probability of Passing Quiz here:
https://brainly.com/question/30308932
#SPJ4
I need help plz!!!!!!!
Answer:
Lorena will have more money in six weeks.
She will have $8 more
Step-by-step explanation:
Please give brainliest
In this question we will solve a simplified version of the Grossman model. Suppose utility is U(H
t
,Z
t
)=Z
t
×H
t
. The production function for health is H
t
= M
t
+H
t−1
and production for the home good is Z
t
=J
t
(Hint: Notice these are not functions of T
H
or T
Z
). The price of M
t
is 2$ per unit and the price of J
t
is 1$ per unit. The individual works a fixed amount of time, T
W
=5 at wage w=2$ per unit of time (Hint: we are assuming T
W
is fixed and not a choice). Previous periods health, H
t−1
=1. There is no time constraint in this example. For the remaining, we focus on a single period and assume the future does not impact decisions today. 1. What is the budget constraint in this period? 2. Now we will solve for the optimal allocation of health and the home good. Steps; (a) Calculate the first order conditions of the utility function and set them equal to zero. (b) Combine this with the budget constraint and solve for the optimal level of H and Z. 3. Now suppose health depreciates at rate γ=0.75. How may we incorporate this into our model? Solve the new optimal choice of H
t
and Z
t
, and provide and explain the intuition for why the changes occurs.
1. The budget constraint in this period is given by 2H + Z = 10.
2. The optimal allocation of health (H) and the home good (Z₁) is H = (5/3)w and Z₁ = (5/3)w, respectively.
3. Incorporating health depreciation at a rate of 0.75, the new optimal choice is H = 6.25 and Z₁ = (5/3)w.
4. When the individual becomes twice as efficient at producing health with Me, the new optimal choices are H = 6.25 + 2Me and Z₁ = (5/3)w.
5. When the wage rises to $3 per unit time, the optimal choices of H₂ and Z remain the same as in the previous case (H = 6.25 + 2Me and Z₁ = (5/3)w) as there is no impact on the relative prices and production functions.
The budget constraint in this period can be defined as 2H + Z = 5w. Since the individual works a fixed amount of time, TW = 5, and the wage is $2 per unit of time, the total income available for the individual is 5w.
To find the optimal allocation of health (H) and the home good (Z), we need to calculate the first-order conditions of the utility function and set them equal to each other.
∂U/∂H = Z₁ = λ
∂U/∂Z = H = λ
Setting these equal to each other, we get:
Z₁ = H
Combining this with the budget constraint:
2H + Z = 5w
Substituting Z₁ = H into the budget constraint, we have:
2H + H = 5w
3H = 5w
H = (5/3)w
Substituting H back into Z₁ = H, we get:
Z₁ = (5/3)w
Therefore, the optimal level of health (H) is (5/3) times the wage (w), and the optimal level of the home good (Z₁) is also (5/3) times the wage (w).
To incorporate health depreciation at a rate of y = 0.75, we need to modify the production function for health. The new production function becomes:
H₁ = (1 - y)H₋₁ + Mt
Substituting the given values, H₋₁ = 1 and TW = 5, we have:
H₁ = (1 - 0.75) + 5
H₁ = 1.25 + 5
H₁ = 6.25
Therefore, the new optimal level of health (H) is 6.25, and the optimal level of the home good (Z₁) remains the same as before, which is (5/3) times the wage (w).
The intuition behind the change is that since health depreciates, the individual needs to allocate more resources towards producing health to maintain the same level of utility. As a result, the optimal level of health increases.
If the individual becomes twice as efficient at producing health with Me (while keeping the depreciation rate), the new production function for health becomes:
H₁ = (1 - y)H₋₁ + 2Me + Mt
Substituting the given values, H₋₁ = 1 and TW = 5, we have:
H₁ = (1 - 0.75) + 2Me + 5
H₁ = 1.25 + 2Me + 5
H₁ = 6.25 + 2Me
Therefore, the new optimal level of health (H) is 6.25 + 2Me, and the optimal level of the home good (Z₁) remains the same as before, which is (5/3) times the wage (w).
The intuition behind the change is that the increased efficiency in producing health with Me allows the individual to produce more health with the same amount of resources. As a result, the optimal level of health increases further.
If the wage (w) rises to $3 per unit of time, the new budget constraint becomes:
2H + Z = 5w
2H + Z = 5(3)
2H + Z = 15
To find the new optimal allocation of health and the home good, we need to solve for H and Z using the updated budget constraint. However, since the production functions for health and the home good remain unchanged, the optimal level of health (H) and the optimal level of the home good (Z₁) will still be the same as in the previous cases.
The intuition behind this is that when the wage increases, the individual's income increases, allowing them to afford more of both health and the home good. However, the optimal allocation of resources between health and the home good remains unchanged because the relative prices of Me and J, as well as the production functions, are not affected by the increase in the wage.
The complete question:
In this question we will solve a simplified version of the Grossman model. Suppose utility is U (Ht, Zt) = Z₁ × Ht. The production function for health is H₁ = Mt + Ht-1 and production for the hom.................t (Hint: Notice these are not functions of TH or T2). Th........me constraint in this example. For the remaining, we focus on a single ...ssume the future does not impact decisions today.
1. What is the budget constraint in this period?
2. Now we will solve for the optimal allocation of health and the home good. Steps;
(a) Calculate the first order conditions of the utility function and set them equal toeach other.
(b) Combine this with the budget constraint and solve for the optimal level of H andZ.
3. Now suppose health depr......n the intuition for why the changes occurs.
4. In we learne......e version of the model from
3. and explain happens to o.......he model and multiply Me by 2 in the production function.) Explain the intuition for why the changes occurs.
5. We know that education ......odel from 4.)
Learn more about Grossman model: https://brainly.com/question/33485556
#SPJ11
Pls help me the answer
Answer:
The slope is 5/3
Step-by-step explanation
The slope formula is \(\frac{rise}{run}\)
If you take 2 points on the line, the rise is 5 and the run is 3.
In football, the path that a defender must run to
tackle the ball carrier is called the path of pursuit.
If the ball carrier runs 40 yards to the end zone
and the path of pursuit is 45 yards, how far
apart were the ball carrier and defender when
they started? Answer with appropriate
precision.
The surface area of a sphere is 200.96 square centimeters. What is the approximate volume of the sphere? Use 3.14 for π. Round your answer to the nearest hundredth.
Answer:
\(267.95 cm^3\)
Step-by-step explanation:
We need to first find the radius of the sphere.
The surface area of a sphere is given as:
\(A = 4\pi r^2\)
where r is the radius
Therefore:
\(200.96 = 4 * 3.14 * r^2\\\\=> r^2 = 200.96 / 12.56\\\\r^2 = 16\\\\r = \sqrt{16} \\\\r = 4cm\)
The radius of the sphere is 4 cm.
The volume of a sphere is given as:
\(V = \frac{4}{3} \pi r^3\)
Therefore, the volume of the sphere of radius 4 cm is;
\(V = \frac{4}{3} * 3.14 * 4^3\\\\V = 267.95 cm^3\)
The volume of the sphere is \(267.95 cm^3\)
Answer:
C: 267.95 cm3
Step-by-step explanation:
what is angle D? i don't know how to do the math due to being absent on a friday
Answer:
∠ D = 110°
Step-by-step explanation:
Assuming the quadrilateral is a parallelogram.
• Consecutive angles sum to 180° , then
∠ B + ∠ C = 180 , that is
5x + 3x + 4 = 180
8x + 4 = 180 ( subtract 4 from both sides )
8x = 176 ( divide both sides by 8 )
x = 22
Then
∠ B = 5x = 5 × 22 = 110°
• Opposite angles are congruent
∠ D = ∠ B = 110°