The height of the object 1 second after it was launched is equals to 243.1 feet.
Let the launching velocity /initial velocity = u ft./s
and final velocity = 0 feet/sec , because at the maximum height, the final velocity of launching is '0'.
Maximum height , s = 3136 feet
time, t = 14 sec
Using the Equation of motion,
v² - u² = -2gs
where, v --> final velocity
u --> initial velocity
g --> acceleration due to gravity and it is a constant with value 9.8 m/sec²
s --> distance ( max. height)
plugging all known values in above formula,
0 - u² = -2 (9.8)(3136) = - 61465.6
=> - u² = - 61465.6
=> u² = 61465.6
=> u = √61465.6 = 247.92 ~ 248
=> u = 248 feet/sec
Now, the height, in feet, of the object 1 second after it was launched is
s = ut + (1/2)(-g)t²
=> s = 248(1) + (1/2)(-9.8)(1)
=> s = 248 - 4.9 = 243.1 feet
So, the required height is 243.1 feet.
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Find the equation of the straight line that has a slope of 4 and passes through the point (-1, -6)
Answer:
y = 4x - 2
Step-by-step explanation:
y = 4x + b
-6 = 4(-1) + b
-6 = -4 + b
b = -2
y = 4x - 2
Answer:
[tex]y - (-6) = 4(x - (-1))[/tex] or [tex]y = 4x - 2[/tex]
Step-by-step explanation:
We can use point slope form: [tex]y - y_{1} = m(x - x_{1})[/tex], where [tex](x_1, y_1)[/tex] is a point on the line and [tex]m[/tex] is the slope.
We plug in (-1, -6) and 4 to get: which simplifies to [tex]y + 6 = 4(x + 1)[/tex]
If we want to express this in the form y = mx + b, we have to do a little rearranging. [tex]y + 6 = 4(x + 1)[/tex] becomes [tex]y + 6 = 4x + 4[/tex] and then we subtract 6 from both sides to get: [tex]y = 4x - 2[/tex]
The question is below, please answer. This is in a hurry!
Answer:
A)
Step-by-step explanation :
This question isn't too hard, but you would have to use similar triangles.
Fred works for $11.25 per hour. His regular hours are 40 hours per week and he gets time and a half for overtime. One week he works 48.5 hours. He wants to calculate his pay. Complete the table.
rate: $11.25, regular hours:--------------, overtime: N/A, total: $----------
rate: $--------, regular hours: N/A, overtime: ---------, total: $----------
gross: $----------
Fred's pay for the specified week, with a rate of $11.25 for regular hours and time and a half for overtime, and number of hours worked of 48.5 hours is presented by completing the attached table as follows;
Rate: $11.25, regular hours: 40, overtime: N/A, total: $450
Rate: $16.875, regular hours: N/A, overtime: 8.5, total: $143.4375
Gross: $593.4375
What is a payment rate?A payment rate is the amount of payment or money that is received in a unit of time.
The amount Fred earns per hour = $11.25
The number of regular hours Fred works per week = 40
The rate at which he is paid for overtime = Time and a half
The number of hours Fred works in the specified week = 48.5 hours
Therefore, the amount Fred earns for working overtime = 1.5 × $11.25 = $16.875
The amount Fred earns for regular hours during the specified week = 40 × $11.25 = $450
The number of overtime hours Fred works for during the week = 48.5 - 40 = 8.5
The amount Fred earns for the overtime work = 8.5 × $16.875 = $143.4375
Fred's gross payment for the week is therefore; $450 + $143.4375 = $593.4375
The table can therefore be completed by plugging in the above values as follows;
Rate: $11.25, regular hours: 40, overtime: N/A, total: $450
Rate: $16.875, regular hours: N/A, overtime: 8.5, total: $143.4375
Gross: $593.4375
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a scoop of premium ice cream has 5 grams of protein, 21 grams of carbohydrate, and 22 grams of fat. how many total calories will this provide? a. 48 calories b. 100 calories c. 192 calories d. 302 calories
The total calories from the ice cream are 302 kcal when a scoop of quality ice cream has 5 grams of protein, 21 grams of carbohydrate, and 22 grams of fat.
What is nutrition ?A vital component of wellbeing and growth is nutrition. Strengthened immune systems, safer pregnancies and deliveries, a decreased risk of non-communicable diseases, and longer life spans are all associated with better nutrition. Healthy kids learn more effectively.
calculation
Since we know that every gram of protein includes 4 kcal, 5 g will have 5 × 4 = 20 kcal.
According to our knowledge, each gram of carbohydrate carries 4 kcal, so 21g will contain 21 x 4 = 84 kcal.
Given that each gram of fat has 9 calories, 22 grams will have a caloric value of 22 x 9 = 198 calories.
20 + 84 + 198 = 302 kcal are the total calories from the ice cream.
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A, B & C form the vertices of a triangle, where
∠CAB = 90°.
AB = 10.2 m and AC = 4.9m. Evaluate
∠ ACB, giving your answer rounded to 3 SF.
Answer:
Step-by-step explanation: To find the measure of angle ACB, we can use the Pythagorean Theorem: AB^2 + AC^2 = BC^2.
Substituting in the given values for AB and AC, we get: 10.2^2 + 4.9^2 = BC^2
Solving for BC, we get: BC = √(10.2^2 + 4.9^2)
Substituting this value back into the equation for the Pythagorean Theorem, we get:
AB^2 + AC^2 = (√(10.2^2 + 4.9^2))^2
Simplifying this equation, we get:
AB^2 + AC^2 = 10.2^2 + 4.9^2
This equation is already in the correct form, so we can solve for ∠ACB directly:
∠ACB = tan^-1(AC/AB)
Substituting in the given values for AC and AB, we get:
∠ACB = tan^-1(4.9/10.2)
Using a calculator, we find that tan^-1(4.9/10.2) is approximately equal to 26.7°.
Rounded to 3 significant figures, this value is 26.7°.
Find the gradient vector field of f and sketch it:
f(x,y)= √(x2+y2)
The gradient vector field of f is ∇(f) = (xi+yj)/√(x^2+y^2) ans sketch is given below.
In the given question, we have to find the gradient vector field of f and sketch it.
f(x,y)= √(x^2+y^2)
To find the gradient, it's just the partial derivatives for x and y
∇(f) = ∂f/∂x i + ∂f/∂y j
In this case, we have
∂f/∂x = x/√(x^2+y^2) and ∂f/∂y = y/√(x^2+y^2). So
∇(f) = x/√(x^2+y^2) i + x/√(x^2+y^2) j
We can write it as
∇(f) = (xi+yj)/√(x^2+y^2).
This is a unitary vector field everywhere, with the exception of the origin, where it is undefined, where we can see it as the vector xi+yj divided by the magnitude √(x^2+y^2). From the starting point, the direction is outward.
The sketch is given below:
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If the simple interest on 4000$ for 6 years is 1440$ then, what is the interest rate?
The rate of interest for the given data can be found as 6%.
What is simple interest?Simple interest can be defined as a form of interest in which the percent rate is applied on the same principal for a given period of time. The amount can be calculated by adding the interest to the principal.
The given data as per the question is as below,
P = $4000, t = 6 years and Interest = $1440.
Suppose the rate of interest be r% per annum.
Substitute all the values in the expression for simple interest (P × r × t)/100 as follows,
1440 = (4000 × 6 × r)/100
⇒ r = 6%
Hence, the rate of interest is obtained as 6%.
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What does the missing number equal to?
The missing number is equal to 42
Let the missing number be 'x'
Therefore, we have the equation as
[tex]\frac{2}{35} = \frac{1}{30} + \frac{1}{x}[/tex]
Solving this equation further, we have
[tex]\frac{1}{x} = \frac{2}{35} - \frac{1}{30}[/tex]
Taking L.C.M. on R.H.S. side, we have
[tex]\frac{1}{x} = \frac{(2)(30) - (1)(35)}{(30)(35)}[/tex]
[tex]\frac{1}{x} = \frac{60 - 35}{1050}[/tex]
[tex]\frac{1}{x} = \frac{25}{1050}[/tex]
[tex]\frac{1}{x} = \frac{1}{42}[/tex]
On cross multiplying this equation, we get
[tex]x = 42[/tex]
Therefore, we can say that the missing number is equal to 42.
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m and p are in direct proportion.
The equation of proportionality is m = 8p.
If p increases from 3 to 7, how much will m increase by?
If your answer is a decimal, give it to 1 d.p.
M will increase from 24 to 56
What is meant by direct proportion ?The relationship between two values where their ratio equals a constant number is known as a direct proportion or direct variation. It is symbolised by the proportional sign ().
According to the direct proportion formula, if y is directly proportional to x, we can state that y = kx, where k is a constant. Y = kx also serves as the direct proportion equation's general form.
When one quantity increases or declines, the other quantity also rises or falls in direct proportion. On the other hand, in indirect or inverse proportion, if one quantity rises, the other one falls, and vice versa.
m= 8p
When p = 3
m =3 × 8 =24
When p = 47
m=8× 7 = 56
So M will increase from 24 to 56
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One half times ? Equals ?
where s is weekly sales in dollars and t is the number of weeks since the end of the campaign. (a) find the rate of change of s (that is, the rate of sales decay).
The rate of change of S for the weekly sales is :
-250 000e⁻°·⁵t
Given:
the sales of the product is :
S = 500,000e^-0.5t
where S is the weekly sales in the dollars and t is the number of weeks since end of the campaign.
we are asked to find the rate of sales dS/dt = ?
that is the rate of sales of delay.
Given:
S = 500,000e^-0.5t
dS/dt =(500,000)e^-0.5t + 500,00 (e^-0.5t)
= 0 + 500,00 (e^-0.5t)
= - 250 000 e^0.5t
therefore, dS/dt = - 250 000 e^0.5t
Hence we get the required answer.
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suppose it takes you 1414 hour to drive to the movie theater at a rate of 40 mph. your friend lives closer to the movie theater than you do. which inequality represents the distance d, in miles, that your friend lives from the movie theater?
Answer:
Step-by-step explanation:
xdd
xddd
xdd
xd
xddd
What is the gradient of the
line that passes through the
points (0,0) and (3, 12)?
m=
Submit Answer
Answer:
4
Step-by-step explanation:
gradient = slope = m = rise / run
from the origin (0,0) this line rises '12' and has a run of '3'
12/3 = 4
a poll was conducted two weeks before an election and showed that the incumbent would win with 54% of the vote, with a 3% margin of error. what is the confidence interval for this poll?
The confidence interval for the given poll is; 51% to 57%
How to find the confidence Interval?We are given that;
Sample proportion; p = 54% = 0.54
Margin of error; E = 3% = 0.03
Now, formula for confidence interval of proportions is;
p ± E
where;
p is sample proportion
E is margin of error
Thus;
CI = 0.54 ± 0.03
CI = (0.54 - 0.03), (0.54 + 0.03)
CI = (0.51, 0.57)
We conclude that the confidence interval is CI = (0.51, 0.57)
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The system of equations is graphed on the
coordinate plane.
y=-1/2x-1
y=1/4x-4
Enter the coordinates of the solution to the system of
equations in the boxes.
Answer:
[tex](4,-3)[/tex]
Step-by-step explanation:
The solution is where the graphs intersect.
Плиз сделайте даю 20 баллов
Answer:
sorry I don't know now how to read
solve by graphing. please show work
The graph is a parabola with its touching the x-axis at (3,0)
What is a parabola?A parabola is a curve where any point is at an equal distance from:
a fixed point (the focus ), and
a fixed straight line (the directrix )
its general equation is y = a(x – h)² + k or x = a(y – k)² +h. Here (h, k) denotes the vertex. y = a(x – h)2 + k is the regular form. x = a(y – k)2 +h is the sidewise form.
Given here (x-3)² + 4 = -4/9(x(x-6))
simplifying this we get
9(x²-6x+13) = -4 (x(x-6))
13x²-78x+117 = 0
(x-3)² = 0
thus it has a root at x=3
The graph is attached showing the parabola touching the x-axis at (3,0)
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The mass of a cleaning liquid in a bottle is 459 g.
The density of the liquid is 0.9 g/cm3.
How many ml of liquid are in the bottle?
Answer:
There's 413.1ml of liquid in the bottle
Michael’s class grew plants as part of the experiment. Michael’s plant grew 1/12 inch in the first week, 3/12 of an inch in the second week, and 5/12 of an inch in the third week. How much did Michael’s plant grow in those three weeks?
Answer:
{ No SIMPLIFIED: [tex]\frac{9}{12} inches[/tex] }
{ SIMPLIFIED: [tex]\frac{3}{4} inches[/tex] }
Step-by-step explanation:
If we want to know about the plant grows, we need to add the fractions in 3 weeks with this solution:
[ The inch of the plant 1st week ] + [ The inch of the plant 2nd week ] + [ The inch of the plant 3rd week ] = [ The inch of the plant in 3 weeks ]
Look at the denominator of 3 weeks, it is 12 and the numerators are 1,3,5
To plus the fraction we remain the denominator and plus the numerators together which we can result in this equation:
[tex]\frac{1}{12}[/tex] + [tex]\frac{3}{12}[/tex] + [tex]\frac{5}{12}[/tex] = [tex]\frac{1 + 3 + 5}{12}[/tex] = [tex]\frac{9}{12}[/tex] { SIMPLIFIED: [tex]\frac{9 : 3 }{12 : 3} = \frac{3}{4}[/tex] }
So then we see that if you choose no simplified then: Michael's plant grow [tex]\frac{9}{12}[/tex] inches in 3 weeks or you could choose the simpliflied one then: Michael's plant grow [tex]\frac{3}{4}[/tex] inches in 3 weeks.
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how would you change the test procedure of part (b) to obtain a test with significance level .05? what impact would this change have on the error probability of part (c)?
the impact on the error probability of part is on Decreasing trends of the test procedure
A Type II error is when we fail to reject a false null hypothesis. Higher values of α make it easier to reject the null hypothesis, so choosing higher values for α can reduce the probability of a Type II error.
The consequence here is that if the null hypothesis is true, increasing α makes it more likely that we commit a Type I error (rejecting a true null hypothesis).
So using lower values of α can increase the probability of a Type II error.
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in the united states, about what percentage of people age 65 or older take at least five prescription medicines daily?
Approximately 50% percentage of people age 65 or older take at least five prescription medicines daily in the United States.
In the United States, approximately 50% percentage of people aged 65 or older take at least five prescription medicines daily. This figure is based on data from the Centers for Disease Control and Prevention (CDC) which track and analyze the health and healthcare of the US population. The CDC found that in 2015, those ages 65 or older reported taking an average of 14.7 prescriptions per person, which is an increase from the average of 13.7 prescriptions per person in 2010. Of those aged 65 or older, 50% reported taking at least five medications daily, while 25% reported taking at least 10 medications daily. The data also showed that seniors were more likely to take multiple medications if they had chronic conditions such as diabetes, high blood pressure, and heart disease. This highlights the importance of closely monitoring and managing medication use, especially among seniors, to ensure that their medications are appropriate and safe.
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The temperature at 8 a. M. I 3. 3°C. At 4 p. M. , the temperature i 7. 22°C. What i the change in temperature from 8 a. M. To 4 p. M. ? Enter the correct anwer in the box. Subtract to find the change in temperature
To calculate the change in temperature from 8 a. m. to 4 p. m., time we need to subtract the temperature at 8 a. m. from the temperature at 4 p. m. 7.22°C - 3.3°C = 4.92°C Therefore, the change in temperature from 8 a. m. to 4 p. m. is 4.92°C.
To calculate the change in temperature from 8 a. m. to 4 p. m., we need to subtract the temperature at 8 a. m. from the temperature at 4 p. m. The temperature at 8 a. m. was 3.3°C, and the temperature at 4 p. m. was 7.22°C. Subtracting 3.3°C from 7.22°C gives the change in temperature of 4.92°C. To calculate the change in temperature from 8 a. m. to 4 p. m., we need to subtract the temperature at 8 a. m. from the temperature at 4 p. m. 7.22°C - 3.3°C = 4.92°C This means that the temperature increased by 4.92°C from 8 a. m. to 4 p. m. by time . The answer to the question is 4.92°C.
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suppose a 90% confidence interval for the population mean resulted in an upper limit of $658 and a lower limit of $273. what is the correct interpretation of this confidence interval?
This confidence interval suggests that we are 90% confident that the population mean lies between $273 and $658.
This confidence interval provides us with an estimate of the population mean with 90% confidence. This confidence interval suggests that we are 90% confident that the population mean lies between $273 and In other words, we can be 90% sure that the population mean falls within this range. This confidence interval does not tell us the actual population mean, but it provides us with an estimate of where the population mean is likely to lie. Furthermore, it also provides us with an indication of the degree of uncertainty associated with our estimate.
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Factor X^3-2x^2-8x???
Answer:
x( x-4)(x+2)
Step-by-step explanation:
x^3-2x^2-8x
First factor out the greatest common factor x
x( x^2 -2x -8)
What 2 numbers multiply to -8 and add to -2
-4*2 = -8
-4+2 = -2
x( x-4)(x+2)
Which function models the data in the table below?
y = -1/2x + 5
y = -2x + 5
y = -1/2x + 10
y = -2x + 10
The function that models the data in the given table is: D. y = -2x + 10.
How to Write the Function that Models the Data in a Table?The function that models the data of a table can be expressed in the slope-intercept form as y = mx + b, where:
the slope = m = change in y / change in x.y-intercept = b.Find the slope of the function using two pairs of values from the table, (6, -2) and (10, -10):
Slope (m) = change in y / change in x = (-10 - (-2)) / (10 - 6)
Slope (m) = -8 / 4
Slope (m) = -2
Find the y-intercept (b) by substituting m = -2 and (x, y) = (6, -2) into y = mx + b:
-2 = -2(6) + b
-2 = -12 + b
-2 + 12 = b
10 = b
b = 10
To write the function, substitute m = -2 and b = 10 into y = mx + b:
y = -2x + 10
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determine if the line integral of the vector field sketched in the figure along the curve c is positive, negative, or zero.
The line integral of the vector field in the figure is zero. This is due to the fact that the vector field is perpendicular to the curve c, and therefore, the integral of the dot product of the vector field and the tangent vector along the curve c is zero.
1. The line integral of a vector field is the integral of the dot product of the vector field and the tangent vector of the curve along the curve.
2. The vector field in the figure is perpendicular to the curve c.
3. The dot product of two perpendicular vectors is zero.
4. Therefore, the integral of the dot product of the vector field and the tangent vector along the curve c is zero.
5. Hence, the line integral of the vector field in the figure is zero.
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3x - 7 = 20 Solve for x please i have a 6.3 in math
Answer: x = 9 (I think)
Step-by-step explanation:
3x - 7 + 7 = 3x
20 + 7 = 27
3x = 27
3x ÷ 3 = x
27 ÷ 3 = 9
x = 9
-1/2p - 4< 3
Please try to graph on number line
We can begin by rewriting the problem:
3/4 - 1/2p > 5/4
Let’s solve accordingly through steps:
1. Subtract 3/4
-1/2p > 2/4
2. Divide both sides by the coefficient
-1/2 / -1/2 = p
2/4 / -1/2 = -1
3. Simplify & Switch Signs
p < -1
The answer to Part A is p < -1.
Part B: On a number line, this answer would be graphed by plotting a point at -1 and drawing an arrow that goes to the left direction to show that p is less than -1.
Systolic blood pressure readings are normally distributed with a mean of 121 and a standard deviation of 15.
Find the z-score to the nearest tenth for the following blood pressure readings.
a. 142 _____ANSWER HERE_
b. 130 _____ANSWER HERE_
c. 103 _____ANSWER HERE_
The z-score to the nearest tenth for the following blood pressure readings is 45.14%.
What is blood pressure ?
The force of moving blood exerted on the walls of blood arteries is known as blood pressure. The heart's action of pumping blood through the circulatory system is mostly responsible for this pressure. The pressure in the major arteries is meant when the word "blood pressure" is used without qualifier.
As the data is normally distributed we can use standard normal z table to estimate the answers.
Z = (x-mean)/s.d
Given mean = 121.
S.d = 15.
P(X<142).
Z = (142-121)/15 = 1.4
From z table,
P(z<1.8) = 0.9641 ~ 96.41%
P(X>130).
Z = (130-121)/15 = 0.6
From z table,
P(z>0.6) = 0.8849
P(112<X<130) = P(X<130)-P(X<112).
P(X<130).
Z = (130-121)/15 = 0.6
From z table,
P(z<0.6) = 0.7257
P(X<112).
Z = (112-121)/15 = -0.6
From z table,
P(z<-0.6) =0.2743
Required answer is 0.7257-0.2743 = 0.4514 ~ 45.14%
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Pablo has drawn Parallelogram ABCD and its diagonals, AC and BD. Using Side-Side-Side, he has proven that A BAD is congruent to A DCB.
Given this, which result is Pablo now able to prove?,
O ABOCAAOB
O ACOB
AAOD
O ZCOB is an acute angle.
O The area of A BOC is equal to the area of A AOB.
Answer:
Step-by-step explanation: