The calculation of 129 ÷ 3.332 rounded to the appropriate number of significant digits is 39.
What is division of the two numbers?
Given that;
129 ÷ 3.332
First we convert 3.332 to fraction
3.332 = 3.332/1
3.332 = 3.332/1 × 1000/1000 = 3332/1000
3.332 = 833/250
Hence we have;
129 ÷ 833/250
This can be written as
= 129 × 250/833
= 32250/833
= 38.71549 ≈ 39
Therefore, the calculation of 129 ÷ 3.332 rounded to the appropriate number of significant digits is 39.
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A suitcase measures 18 inches long and 12 inches high. What is the diagonal length of the suitcase?
Answer:
21.6 in
Step-by-step explanation:
Imagine the suitcase as a rectangle, with length of 18 in and width of 12 in. In order to find the diagonal length, simply use the Pythagorean Formula, a^2 + b^2 = c^2, and solve for c!
In this case, a = 18 and b = 12.
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graph F(x) = |x - 1|
Draw the graph:
f(x) = |x-1|
f(x) = -(x-1) when x-1 is negative
f(x) = (x-1) when x-1 is positive
when x = -2, f(x) = 3
when x = -1, f(x) = 2
when x = 0, f(x) = 1
when x = 1, f(x) = 0
when x = 2, f(x) = 1
Using this values, draw the graph of f(x) = |x-1|
Hence, the required modulus of x-1 graph.
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yolanda drove 638 miles in 11 hours at the same rate how many miles would she drive in 13 hours
Answer: 754
Step-by-step explanation:
Divide 683/11 to get the unit rate of 58. That means she is driving 58mph.
Multiply that by how many hours you have, 13, and you get 754.
Help, please
A rectangular room is 1.2 times as long as it is wide, and its perimeter is
30 meters. Find the dimension of the room.
length___
Width is____
The width of the rectangle is 6.82 meters, while the length of the rectangle is 8.184 meters.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
Let the width of the rectangle be x.
Given that a rectangular room is 1.2 times as long as it is wide. Therefore, the length is 1.2x.
Perimeter = 2(x + 1.2x)
30 meters = 2(2.2x)
30 = 4.4x
x = 6.82
Hence, the width of the rectangle is 6.82 meters, while the length of the rectangle is 8.184 meters.
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Find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1 z=-0.92 z=1.23
The area of the shaded region for a z-score of -0.92 is 0.1788, which means the area that will be shadeded in the normal distribution graph is 17.88% of the total.
What is Normal Distribution?The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.
1.) The area of the shaded region for a z-score of -0.92 is 0.1788, which means the area that will be shadeded in the normal distribution graph is 17.88% of the total.
2.) The area of the shaded region for a z-score of 1.23 is 0.8907, which means the area that will be shadeded in the normal distribution graph is 89.07% of the total.
Now, the area of the shaded region will be,
Area = 0.8907 - 0.1788
= 0.7119
= 71.19%
Hence, the area of the shaded region is 71.19%.
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Find the equation of the plane passing through the points A=(1,1,1), B=(1,4,5), C=(−3,-2,0).
Find the area of the triangle the 3 points from the first equation.
Find the angle between the 2 vectors; (1) from A to B and (2) from C to B.
Take any two pairs of the given points and make vectors out of them. For example, the vector from A to B is
[tex]\vec v_1 = \langle 1,4,5\rangle - \langle 1,1,1\rangle = \langle0,3,4\rangle[/tex]
and the vector from A to C is
[tex]\vec v_2 = \langle -3,-2,0\rangle - \langle1,1,1\rangle = \langle-4,-3,-1\rangle[/tex]
These vectors lie in the same plane (the one we want). We can get a third vector that is normal to the plane by taking their cross product (details omitted).
[tex]\vec n = \vec v_1 \times \vec v_2 = \langle 9,-16,12 \rangle[/tex]
If [tex]\vec u = \langle x,y,z\rangle[/tex] is an arbitrary vector, then the vector from any of the points A, B, or C to [tex]\vec u[/tex] will lie in our plane. That is, if we start from A,
[tex](\vec u - \langle1,1,1\rangle) \cdot \vec n = 0[/tex]
and this reduces to the equation of the plane,
[tex]\langle x - 1, y - 1, z - 1 \rangle \cdot \langle 9, -16, 12 \rangle = 0[/tex]
[tex]9 (x - 1) - 16 (y - 1) + 12 (z - 1) = 0[/tex]
[tex]\boxed{9x - 16y + 12z = 5}[/tex]
Area of triangle ABCThis follows immediately from the cross product identity
[tex]\|\vec x \times \vec y\| = \|\vec x\| \|\vec y\| \sin(\theta)[/tex]
where [tex]\theta[/tex] is the angle between [tex]\vec x[/tex] and [tex]\vec y[/tex]. The left side corresponds to the area of the parallelogram spanned by [tex]\vec x[/tex] and [tex]\vec y[/tex]; half of this area would be that of a triangle. (see attached)
In our case, we have
[tex]\|\vec n\| = \|\vec v_1 \times \vec v_2\| = \sqrt{481}[/tex]
so the area of ABC is [tex]\boxed{\dfrac{\sqrt{481}}2}[/tex].
Angle between A to B and between C to BWe already know the first vector, [tex]v_1[/tex].
The vector from C to B is
[tex]\vec v_3 = \langle 1,4,5 \rangle - \langle -3,-2,0 \rangle = \langle 4, 6, 5 \rangle[/tex]
Recall the dot product identity,
[tex]\vec x \cdot \vec y = \|\vec x\| \|\vec y\| \cos(\theta)[/tex]
Then
[tex]\vec v_1 \cdot \vec v_3 = \|\vec v_1\| \|\vec v_3\| \cos(\theta) \implies \cos(\theta) = \dfrac{38}{5\sqrt{77}} \implies \theta \approx \boxed{29.9914^\circ}[/tex]
Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future; however, its value depreciates monthly. The expression shows the depreciated sales value of the gadget: 2,020 − 22m
What does the coefficient of the expression represent? The number of months Megan will wait to sell the gadget The monthly depreciation value of the gadget The amount of money Megan will get when she sells the gadget The original value of the gadget
The coefficient (m) of the expression represents: C. the monthly depreciation value of the gadget.
What is depreciation?Depreciation can be defined as a process in which the monetary value of a physical asset decreases or falls over a period of time, especially due to wear and tear.
In this scenario, we can infer and logically deduce that the coefficient (m) of the given expression represents the monthly depreciation value of Megan's gadget.
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Answer:
it is C
Step-by-step explanation:
give the other guy brainliest, I am ok with hearts and good ratings.
1. How many variables are involved in the chi-square test?
2. Which type of chi-square test is this?
A.goodness of fit B.test of independence
3. How many degrees of freedom are involved?
4. Using the chi-square critical values table is the result of this rest statistically significant?
A. Yes B.No
The result of the respective questions are:
This chi-square test only takes into consideration one variable.The type of chi-square test this is is a Goodness of Fitdf= 3NOHow many variables are involved in the chi-square test?a)
This chi-square test only takes into consideration one variable.
b)
The type of chi-square test this is, is a Goodness of Fit
To test the hypothesis, we must determine whether the actual data conform to the assumed distribution.
The "Goodness-of-Fit" test is a statistical hypothesis test that determines how well the data that was seen resembles the data that was predicted.
c)
Parameter
n = 4
Therefore
Degrees of freedom
df= n - 1
df= 4 - 1
df= 3
d)
In conclusion
Parameters
[tex]\alpha = 0.05[/tex]
df = 3
Hence
Critical value = 7.814728
Test statistic = 6.6
Test statistic < Critical value, .
NO, the result of this test is not statistically significant.
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A well-mixed cookie dough will produce cookies with a mean of 6 chocolate chips apiece. What is the probability of getting a cookie with no more than 3 chips? Round your answer to four decimal places.
The probability of getting a cookie with no more than 3 chips is 0.714.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
Well-mixed cookie dough will produce cookies with a mean of 6 chocolate chips apiece.
Using poison ratio:
[tex]\rm P (X = k) = \dfrac{\lambda^k e^{-\lambda}}{k!}[/tex]
λ is the mean number of chocolate chips in a piece
[tex]\rm P (X = 6) = \dfrac{6^k e^{-6}}{k!}[/tex]
P(X ≥ 5) = 1 - P(X < 5)
P(X ≥ 5) = 1 - P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)
[tex]\rm P(X \geq 5) = 1-[\dfrac{6^0 e^{-6}}{0!}+\dfrac{6^1 e^{-6}}{1!}+\dfrac{6^2 e^{-6}}{2!}+\dfrac{6^3 e^{-6}}{3!}+\dfrac{6^4 e^{-6}}{4!}][/tex]
After solving;
P(X ≥ 5) = 0.714
Thus, the probability of getting a cookie with no more than 3 chips is 0.714.
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The product of two number is 8 . If one of the numbers is 3 1/3 find the other number.
Hello!
Let the missing number be x.
⇒ 3 1/3 × x = 8
⇒ 10/3 × x = 8
⇒ x = 24/10
⇒ x = 12/5
The other number is [tex]\boxed {\frac{12}{5}}[/tex]
Answer:
The other number ia:
12/5
Step-by-step explanation:
3 1/3 = 3 + 1/3 = 9/3 + 1/3 = 10/3
a * 10/3 = 8
a = 8*3/10
a = 24/10
a = 12/5
a = 2.4
Check:
(12/5) * (10/3) = 8
(12*10) / (5*3) = 8
120 / 15 = 8
Find an equation of the line passing through the given points. Use function notation to write the equation,
(-4,9) and (2,-3)
Adi used algebra tiles to represent the product (negative 2 x minus 1)(2 x minus 1).
The true statement is (b) use of incorrect header
How to determine the true statement?The product expression is given as:
(-2x - 1)(2x - 1)
Expand the expression
(-x - x - 1)(x + x - 1)
This means that the header of the algebra tiles would be:
-x, -x, 1 and x, x and -1
From the figure, we can see that this is incorrectly represented
Hence, the true statement is (b)
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ram takes 20 minutes to inspect a car, while robert takes only 18 minutes.if both start inspecting car at 8.00 hours what is the first time at which both will have finished inspecting a car at the same point time
Answer:
11:00
Step-by-step explanation:
here we have to calculate the LCM of 20 and 18
20 = 2² × 5
18 = 2 × 3²
Then
LCM(20 , 18) = 2² × 5 × 3² = 20 × 9 = 180
The
After 180 minutes (3 hours) they will have finished inspecting a car at the same point time.
Then
At 8:00 + 3 = 11:00 Ram and Robert will have finished inspecting a car at the same point time.
Jim weighs 30 pounds less than Tom, and together they weigh 210 pounds. Let n = Tom's weight in pounds.
(n - 30) + n = 210
(n + 30) + n = 180
(n + 30) + n = 210
(n - 30) + n = 180
The equation that represents the given problem would be (n-30) + n = 210. The correct option is the option A; (n-30) + n = 210
What is a linear equation?A linear equation is an equation that has the variable of the highest power of 1.
The standard form of a linear equation is of the form Ax + B = 0.
From the given information,
n = Tom's weight in pounds
If Jim weighs 30 pounds less than Tom
Jim weighs will be (n - 30)
Thus,
The sum of their weight
(n-30) + n
∴ (n-30) + n = 210
Hence, the equation that represents the given problem would be (n-30) + n = 210. The correct option is the option A; (n-30) + n = 210
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A random variable is not normally distributed, but it is mound shaped. It has a mean of 11 and a standard deviation of 4.
If you take a sample of size 14, can you say what the shape of the sampling distribution for the sample mean is? Why?
Using the Central Limit Theorem, nothing can be stated about the shape of the sampling distribution for the sample mean, as the sample size is less than 30.
What does the Central Limit Theorem state?It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.
In this problem, we have a skewed variable and n < 30, hence nothing can be stated about the shape of the sampling distribution for the sample mean.
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witch hazel is listed at 12 per galon, less 34.5%. what is the net cost of the amount needed in filling the prescription
The net cost of the amount needed in filling the prescription is 7.86 per gallon
Net costCost of witch hazel = 12 per gallonDiscount = 34.5%Net cost = 12 - (34.5% of 12)
= 12 - (0.345 × 12)
= 12 - 4.14
= 7.86 per gallon
Therefore the net cost of the amount needed in filling the prescription is 7.86 per gallon
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what is the equation of the line that is paralle to y=3x-8 and passes thur the point (4,-5)
⊰_________________________________________________________⊱
Answer:
The equation is-: y=3xStep-by-step explanation:
[tex]\large\displaystyle\text{$\begin{gathered} \sf{Substitute \ the \ values \ into \ the \ formula \ y-y_1=m(x-x_1)} \\ \sf {parallel \ lines \ have \ same \ slopes, \ thus} \\ \sf{slope \ of \ the \ 2nd \ line = 3}\\ \sf{now \ substitute \ the \ values} \\ \sf {y-(-5)=3(x-4)}\\ \sf{y+5=3(x-4) (It's \ Point-Slope\;Form, \ see \ below \ for \ slope-intercept)}\\ \sf {y+5=3x-12} \\ \sf{y=3x-12-5} \\ \sf{y-3x-17} \end{gathered}$}}[/tex]
[tex]\pmb{\tt{done \ !!}}[/tex]
⊱_________________________________________________________⊰
Divide: StartFraction 5 Over 8 EndFraction divided by three-fourths
The value gotten when 5/8 is divided by 3/4 is 5/6.
What is the value gotten from the division?A fraction is a non-integer that is made up of numerator and a denominator. An example is 5/8. Division is the process of grouping a number into equal parts using another number.
5/8 ÷ 3/4
5/8 × 4/3 = 5/6
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Which is the graph of the line with equation y−6=4(x−3)+2?
Number graph ranging from negative four to three on the x axis and negative five to two on the y axis. A line is drawn on the graph that passes through the points (zero, negative four) and (one, zero).
Number graph ranging from negative three to three on the x axis and negative seven to one on the y axis. A line is drawn on the graph that passes through the points (zero, negative six) and (three, zero).
Number graph ranging from negative three to three on the x axis and negative two to five on the y axis. A line is drawn on the graph that passes through the points (negative one, zero) and (zero, four).
Number graph ranging from negative three to three on the x axis and negative two to five on the y axis. A line is drawn on the graph that passes through the points (negative three, zero) and (zero, four).
The linear equation passes through (0, -4) and (1, 0), so we conclude that the correct option is the first one.
Which is the graph of the given linear equation?
Here we have the linear equation:
y - 6 = 4*(x - 3) + 2
if we rewrite the line in slope-intercept form, we get:
y = 4x - 12 + 2 + 6
y = 4x - 4
Then the y-intercept of the line is (0, -4). And when x = 1, we have:
y = 4*1 - 4 = 0
So the line also passes through (1, 0).
Then the correct option is the first one:
"Number graph ranging from negative four to three on the x-axis and negative five to two on the y-axis. A line is drawn on the graph that passes through the points (zero, negative four) and (one, zero)."
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Find the sum of s = 1 - (1)/(4) + (1)/(6)-(1)/(9)+ (1)/(11)- (1)/(14)...
The sum of the equation is
[tex] \frac{859}{2772} [/tex]
How to find the sum
Given the expression
s = 1 - (1)/(4) + (1)/(6)-(1)/(9)+ (1)/(11)- (1)/(14)
Let's find the LCM, which is 2772
s =
[tex] \frac{2772 - 693 + 462 - 308 +252 - 198}{2772} [/tex]
Add the numerators, do the addition before the substraction
s =
[tex] \frac{859}{2772} [/tex]
Thus, the sum of the equation is
[tex] \frac{859}{2772} [/tex]
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Translate the following from words to an algebraic expression or equation,
denoting the unknown by n.
52a. The express train travels 5 mph faster than the local train.
52b. The length of a rectangle is 7 inches more than its width.
52c. The area of a triangle, if the altitude is twice the base
52d. The sum of 3 consecutive even numbers
52e. 15% of the amount by which a number exceeds 10,000
Answer:
a. n+5
b. n+ 7
c. 1\2(n×2n)
d. n +n+1 n+2
Which of the following has a slope of –2 and a y-intercept of 4?
y = 2x – 4
y = –2x – 4
y = –2x + 4
y = 2x + 4
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Which equation has a slope of -2 and a y-intercept of 4?
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
All of these equations are in [tex]\bf{y=Mx+b}[/tex] form.
The y-int. is b. The slope is M.
[tex]\bf{y\!=\!\!-2x+\!4}[/tex] | put in the values
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=\!\!y=-2x+4}[/tex]
[tex]\LARGE\boxed{\bf{aesthetics\not1\theta l}}[/tex]
100POINTS WHY NOT
sally took money from her bank account to go out of town for an audition.she spot 54$ for a round trip ticket and 1/2 of the remaining money on her hotel bill.she spent $7.90 for food and arrived home with $15.10.How much money did Sally take from her bank account??
Answer:
$100
Step-by-step explanation:
Given information:
$54 = cost of ticketCost of hotel = 1/2 remaining money after purchase of ticket$7.90 = cost of food$15.10 = remaining moneyLet x = money taken from bank account
If Sally paid $54 for her ticket, then the money remaining at that point can be defined as: [tex]x-54[/tex]
If the cost of the hotel was half of the remaining money, then:
[tex]\textsf{Cost of hotel}=\dfrac{1}{2}(x-54)}[/tex]
To find how much money Sally took from her bank account, create an equation with the given information and solve for x.
[tex]\implies \textsf{Money in bank} - \textsf{ticket} - \textsf{hotel} - \textsf{ food} =\textsf{remaining money}[/tex]
[tex]\implies x - 54 - \dfrac{1}{2}(x - 54)-7.90=15.10[/tex]
[tex]\implies x - 54 - \dfrac{1}{2}x+27-7.90=15.10[/tex]
[tex]\implies \dfrac{1}{2}x-34.90=15.10[/tex]
[tex]\implies \dfrac{1}{2}x=50[/tex]
[tex]\implies x=100[/tex]
Therefore, Sally took $100 from her bank account.
solve the equation cos (x/2) = cos x + 1. what are the solutions on the interval 0° ≤ x < 360°?
Answer:
Step-by-step explanation:
cos (x/2)=cos x+1
cos (x/2)=2cos ²(x/2)
2 cos²(x/2)-cos (x/2)=0
cos (x/2)[2 cos (x/2)-1]=0
cos (x/2)=0=cos π/2,cos (3π/2)=cos (2nπ+π/2),cos(2nπ+3π/2)
x/2=2nπ+π/2,2nπ+3π/2
x=4nπ+π,4nπ+3π
n=0,1,2,...
x=π,3π
or x=180°,540°,...
180°∈[0,360]
so x=180°
or
2cos(x/2)-1=0
cos (x/2)=1/2=cos60,cos (360-60)=cos 60,cos 300=cos (360n+60),cos (360n+300)
x/2=360n+60,360n+300
x=720n+120,720n+300
n=0,1,2,...
x=120,300,840,1020,...
only 120° and 300° ∈[0,360°]
Hence x=120°,180°,300°
MATH: EXPONENTIAL WORK PROBLEM 1. HELP PLEASE! 13 pts
The amount of the radioactive substance is 374.6 g
How to determine the amount of radioactive substance?The given parameters are:
Initial, a = 424 mgRate, r = 6%Time, t = 2 hoursThe amount of the radioactive substance is calculated as:
A(t) = a(1 - r)^t
This gives
A(t) = 424 * (1 - 6%)^t
At 2 hours, we have:
A(2) = 424 * (1 - 6%)^2
Evaluate
A(2) = 374.6
Hence, the amount of the radioactive substance is 374.6 g
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Set up an algebraic equation and then solve.
The width of a rectangle is 14 units less than the length. If the area is 120 square
units, then find the dimensions of the rectangle.
Length:
Width:
Answer:
Width: 6
Length: 20
Step-by-step explanation:
So the area of a rectangle can be defined as: [tex]A=wl[/tex] where w=width and l=length.
In this case we don't know what the length is, so let's just say the length is the variable l, and since the width is 14 units less than the length, we can express it as (l-14). this gives us the equation: [tex]A=l(l-14)=l^2-14l[/tex]. We can solve for l, since we're given the area which is 120. So let's set the equation equal to that:
Original Equation:
[tex]A=l^2-14l[/tex]
Substitute 120 as A (given)
[tex]120=l^2-14l[/tex]
There is many ways to solve this equation: factoring, quadratic equation, completing the square etc... but in this case I'll just complete the square
Add (b/2)^2 to both sides to complete the square
[tex]120+(\frac{-14}{2})^2=l^2-14l+(\frac{-14}{2})^2[/tex]
Simplify
[tex]169=l^2-14l+49[/tex]
Rewrite right side a square binomial
[tex]169=(l-7)^2[/tex]
Take the square root of both sides
[tex]13=l-7\\[/tex]
Add 7 to both sides
[tex]20=l[/tex]
to solve for width simply subtract 14 from the length which is 20, so the width is 6
Width: 6
L: 20
What is the total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months? a. $25.47 b. $202.55 c. $611.20 d. $4,861.20 please select the best answer from the choices provided a b c d
The total finance charge is $611.20 (Option c) for this compound interest.
Data Given
Principal, P = $4250
Rate of Compound Interest, R = 13.25%
Time, t = 24 months, i.e., 2 years
Since it is compounded monthly, n = 12
Calculating the Total Finance Charge
We know that the formula for total amount of finance charge in a Compound Interest is,
[tex]A=P\frac{r(1+r)^{n} }{(1+r)^{n} - 1}[/tex]
Substituting the values of P, R and n, we get,
[tex]A=4250\frac{13.25(1+13.25)^{24} }{(1+13.25)^{24} - 1}[/tex]
[tex]A = 611.20[/tex]
Thus, the total finance charge is $611.20
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Find the probability of rolling a sum of 7 or 11. (sum of 7 or 11) = _______________
b. Find the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11) = ______________
c. Find the odds against rolling a sum of 7 or 11.
d. In gambling the “odds against” (or “odds on”) usually expresses how much you can gain with a win for each
dollar you bet. If you make a $10 bet that you will roll a sum of 7 or 11, and the dice land on a sum of 7 or 11,
how much money will you win? Include your winnings plus your initial bet.
a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11) is 2/9. b. the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11) is 7/9.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The probability of getting a total of 7 = 6/36
The probability of getting total of 11 = 2/36
a. The probability of rolling a sum of 7 or 11. (sum of 7 or 11)
= 6/36 + 2/36
= 2/9
b. Find the probability of not rolling a sum of 7 nor 11. (not sum of 7 nor 11)
= 1- 2/ 9
= 7/9
c. Find the odds against rolling a sum of 7 or 11.
= 2/9
d. The money you will win, If you make a $10 bet that you will roll a sum of 7 or 11, and the dice land on a sum of 7 or 11.
10 x 2/9 = 20/9
10 x 7/9 = 70/9
Thus, The money you will win $10.
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Please help me....trying to get my HS diploma, i did not graduate :(
A ball is thrown in air and it's height, h(t) in feet, at any time, t in seconds, is represented by the equation h(t)=−t2+7t. When is the ball higher than 10 feet off the ground?
A. 2
B. −5≤t≤−2
C. 2≤t≤5
D. −5
When t is between 2 and 5, the ball will be above 10 feet.so answer is:
C. 2 ≤ t ≤ 5
Given, height h(t) = ₋t² ₊ 7t
At what values of time t is the ball 10 feet above the ground = ?
To find out the time we need to set up an inequality.
Inequality expression is given as = ₋t² ₊ 7t ≥ 10
= ₋t² ₊ 7t ₋ 10 ≥ 0
= ₋(t² ₋ 7t ₊ 10) ≥ 0
= t² ₋ 7t ₊10 ≥ 0
Now, factorize the expression and get the factors.
= t² ₋ 2t ₋ 5t ₊ 10 ≥ 0
=t(t ₋ 2) ₋ 5(t ₋ 2) ≥ 0
=(t ₋ 2) (t ₋ 5) ≥ 0
Hence t value ranges from t = 2 and 5.
As a result, when t is between 2 and 5 seconds, the ball will be farther than 10 feet, 2 ≤ t ≤ 5
Learn more about "Inequality equations" here-
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Given f(x)-3x-1 and g(x)-2x-3, for which value of x does g(x)=f(2)?
Answer:
x = 4
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x)=3x-1\\g(x)=2x-3\end{cases}[/tex]
f(2) means substitute x = 2 into function f(x):
[tex]\begin{aligned}g(x) & = f(2)\\ \implies 2x-3 & = 3(2)-1\\2x-3 & = 6-1\\2x - 3 & = 5\\2x - 3 + 3 & = 5 + 3\\2x & = 8\\\dfrac{2x}{2} & = \dfrac{8}{2}\\x & = 4\end{aligned}[/tex]
Therefore, g(4) = f(2).
f(2)
3(2)-16-15so
g(x)=52x-3=52x=8x=4