7x/z=10-r

solve for z

Answer:

40 feet (after 1.5 seconds).

Step-by-step explanation:

The height h of the ball after t seconds is modeled by the function:

\(h(t)=-16t^2+48t+4\)

And we want to determine the ball's maximum height.

Since the given function is a quadratic, the maximum height occurs at the vertex point.

For quadratics, the vertex point is given by the formulas:

\(\displaystyle \Big(-\frac{b}{2a},f\Big(-\frac{b}{2a}\Big)\Big)\)

In this case, a = -16, b = 48, and c = 4.

Therefore, the t-coordinate at which the vertex occurs is:

\(\displaystyle t=-\frac{48}{2(-16)}=\frac{48}{32}=\frac{3}{2}\)

So, the maximum height occurs after 1.5 seconds.

Then the maximum height will be:

\(\begin{aligned}\displaystyle h\Big(\frac{3}{2}\Big)&=-16\Big(\frac{3}{2}\Big)^2+48\Big(\frac{3}{2}\Big)+4\\\\ &=-16\Big(\frac{9}{4}\Big)+24(3)+4\\\\&=-4(9)+72+4\\\\&=40\text{ feet}\end{aligned}\)

So, the maximum of the ball is 40 feet (after 1.5 seconds).

Answer:

x = 1

Step-by-step explanation:

Both equations can be set equal to each other since they are both equal to y:

\(x-10=-4x-5\\5x-10=-5\\5x=5\\x=1\)

equate both equations !

x - 10 = -4x - 5

5x - 10 = -5

5x = 5

x = 1

therefore x = 1

By answering the presented question, we may conclude that Pythagorean 13.15. Therefore, the measure of the hypotenuse is approximately 13.2 cm

The basic Euclidean geometry relationship between a right triangle's three sides is known as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. The Pythagorean Theorem states that a right triangle's hypotenuse, which is the side opposite the right angle, equals the sum of its sides. It is sometimes written in general algebraic notation as a² + b² = c.

We can use the Pythagorean theorem to find the length of the hypotenuse of a right triangle:

c² = a² + b²

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Substituting the given values, we get:

c² = 13² + 2²

c² = 169 + 4

c² = 173

Taking the square root of both sides, we get:

c = √173

Using a calculator, we get

c ≈ 13.15

Rounding to the nearest tenth, we get:

c ≈ 13.2 cm

Therefore, the length of the hypotenuse is approximately 13.2 cm.

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Answer- 9 shelves

In order to find out how many shelves are need we must divided 175 into 20. 175 divided by 20 is 8.75. But, because you cannot have have .75 of a shelf, you have to round this to a whole. This means that 9 shelves will be the least needed number of shelves need to store 175 books. To check this answer 20 books X 8 shelves is 160 books, which means eight shelves can only store 160 books, we will need and additional shelf to store the last 15 books.

HOPE THIS HELPS & GOOD LUCK!

Answer:

D

Step-by-step explanation:

Answer:

here's your answer hope it helps you

Step-by-step explanation:

a. 0930 hrs= 9:30 am

b. 2245 hrs= 22:45pm(10:45 pm).

If demand or annual usage increases by 10 percent, the Economic Order Quantity (EOQ) will increase. The EOQ model is used in inventory management to determine the optimal order quantity that minimizes total inventory costs.

The Economic Order Quantity (EOQ) is a model used in inventory management to determine the optimal order quantity that minimizes total inventory costs. It takes into account factors such as demand, holding costs, and ordering costs. When demand or annual usage increases by 10 percent, it means that more units are being consumed or sold within a given time period.

With an increase in demand, the EOQ will also increase. This is because the EOQ formula takes into consideration the trade-off between holding costs and ordering costs. Holding costs are the costs associated with holding inventory, such as warehousing and insurance, while ordering costs are the costs incurred when placing an order, such as administrative and transportation costs.

When demand increases, more units need to be ordered to meet the higher demand. This results in an increase in ordering costs, as more frequent orders will need to be placed. Consequently, the EOQ will increase to find the new optimal order quantity that balances the increased ordering costs with the holding costs.

In summary, if demand or annual usage increases by 10 percent, the EOQ will increase due to the need to order more frequently to meet the higher demand, resulting in increased ordering costs. This adjustment ensures that the inventory management system remains efficient and cost-effective.

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It could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

The most accurate interpretation of the given confidence interval is as follows:

We are 95% confident that the true difference in mean wait time between Facility A and Facility B falls within the range of 0.32 minutes to 1.47 minutes.

This means that if we were to repeat the study multiple times and calculate a new confidence interval each time, we would expect that approximately 95% of those intervals would contain the true difference in mean wait time between the two facilities.

Furthermore, based on the observed data and the calculated confidence interval, we can conclude that the difference in mean wait time between Facility A and Facility B is likely to be positive, with Facility B having a higher mean wait time than Facility A. However, we cannot say with certainty that the true difference is exactly within this specific range; it could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

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Answer:

2 + i and + √5

Step-by-step explanation:

Since P(x) is a quartic equation, it has 4 roots.

Since 2 - i and -√5 are two of its roots, then its conjugate pairs of 2 + i and + √5 are its other two roots.

So, its other two roots are 2 + i and + √5

Answer:

-59

Step-by-step explanation:

2 is the first digit right after the decimal point. The digit after it is 3, Both digits would round down, therefore meaning that the whole number would still be -59

Graph theory is relevant in the design of network topologies such as roads, satellite air traffic control stations, etc. It helps in analyzing and optimizing network structures.

In the context of a Jamaica road area network managed by the National Works Agency (NWA), graph theory can be applied to study various theoretical properties.

A personalized road graph network with at least 20 nodes is created, and its features are explained based on graph theory principles. Additionally, the Dijkstra matrix is generated to support the properties of the depicted graph.

Graph theory provides a framework for studying and analyzing network structures. In the design of road networks, graph theory concepts can be applied to understand the connectivity, efficiency, and optimization of routes. For example, in the Jamaica road area network managed by the NWA, the personalized road graph network can be created to capture the relationships between different road intersections or nodes. The nodes represent locations, and the edges represent the road segments connecting them.

Theoretical properties of the road graph network can be analyzed using graph theory. These include concepts such as connectivity, shortest paths, degree centrality, and clustering coefficients.

Connectivity determines the connectivity between different parts of the road network, while shortest paths help identify the most efficient routes between nodes. Degree centrality measures the importance of a node in terms of the number of connections it has, and clustering coefficients analyze the presence of clusters or groups of nodes.

To support these properties, the Dijkstra matrix can be generated. The Dijkstra algorithm finds the shortest paths between nodes in a graph, which can be used to construct the Dijkstra matrix.

This matrix provides information about the distances or costs between nodes, aiding in the analysis of the road network's efficiency and connectivity.

In summary, graph theory plays a crucial role in the design and analysis of network topologies, including road networks. The personalized road graph network for the Jamaica road area network demonstrates how theoretical properties can be applied and analyzed using graph theory concepts.

The generated Dijkstra matrix further supports the understanding of the graph's properties, such as connectivity and shortest paths.


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Answer:

360

Step-by-step explanation:

Jose will $360 in interest in three years.

Simple interest is based on the principal amount of a loan or the first deposit in a savings account.

Now it is given that,

Principle amount, P = $1500

Rate of interest, R = 8% = 0.08

Time, T = 3 years

Now, since the simple interest paid in T years  is given as,

S.I = PRT/100

S.I = 1500*8*3/100

S.I =36000/100

S.I = 360

Simple interest paid in 3 years is $360.

Hence,Jose will $360 in interest in three years.

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\(4( \frac{1}{5} x + 7) = 2x - 2\)

\(x = 25\)

The standard equation of a circle is expressed as:

x² + y² + 2gx + 2fy + c = 0

In which:

The given equation of circle is:

x² + y²  – 2x – 8 = 0

Find its centre.

2gx = -2x

2g = -2

g = -1

And, 2fy = 0

f = 0

Thus,

Centre = (-(-1), 0) = (1, 0)

This demonstrates that the circle's centre is on the x-axis.

Now,

r = radius = √g²+f²-C

radius = √1²+0²-(-8)

radius =√9 = 3 units

Thus, radius of circle is found as 3 units.

For the given circle x² + y² = 9,

r² = 9

r = 3 units

As a result, this circle's radius matches that of the circle with equation:

x² + y² = 9.

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1. The ratio of shirts Pete pays for to all shirts is 1000.

2. Pete would pay Ana $8.33 for each shirt.

3. Pete would pay Jun $9600 for the shirt.

To determine what Pete would pay Ana for the shirts, we can use the "Buy 5, Get 1 Free" discount. The ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 (5 shirts paid, and 1 shirt received for free).

To fill in the statements:

1. The ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 of 1200 is ____.

To find the missing value, we can set up the following equation:

5/6 * 1200 = x

Solving for x, we have:

x = (5/6) * 1200 = 1000

So, the ratio of shirts Pete pays for to all the shirts Pete gets is 5:6 of 1200 is 1000.

2. ___ × $10 = $

Pete pays $10 for each shirt. Since the ratio is 5:6, the missing value can be calculated as follows:

5/6 * $10 = $8.33 (rounded to two decimal places)

Therefore, Pete would pay Ana $8.33 for each shirt.

3. What would Pete pay Jun for the shirt?

Pete would pay Jun $8 for each shirt. Since Pete needs 1200 shirts, we can calculate the total amount he would pay Jun as follows:

1200 x $8 = $9600

Therefore, Pete would pay Jun $9600 for the shirts.

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Answer:

x ≈ 27.86

Step-by-step explanation:

Supplement means 180 degrees.

7x - 15 = 180

~Add 15 to both sides

7x = 195

~Divide 7 to both sides

x ≈ 27.86

Best of Luck!

The probability that more than 16 ounces is dispensed in a cup is approximately 0.1587, or about 15.87%.

To solve this problem, we need to standardize the value of 16 ounces using the mean and standard deviation provided. We can do this by calculating the z-score, which is defined as:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, we want to find the probability that more than 16 ounces is dispensed, which can be expressed mathematically as:

P(X > 16)

where X is the random variable that represents the number of ounces of soda dispensed per cup.

To calculate this probability, we first standardize the value of 16 ounces using the mean and standard deviation provided. We have:

z = (16 - 12) / 4 = 1

Now we need to find the area under the standard normal distribution curve to the right of z = 1. We can use a standard normal distribution table or calculator to find this probability. Alternatively, we can use the complement rule, which states that:

P(X > 16) = 1 - P(X ≤ 16)

Since the normal distribution is continuous, we can use the cumulative distribution function (CDF) to find the probability of X being less than or equal to 16 ounces. Using the mean and standard deviation provided, we have:

P(X ≤ 16) = Φ((16 - 12) / 4) = Φ(1) = 0.8413

where Φ(z) is the CDF of the standard normal distribution.

Therefore, using the complement rule, we have:

P(X > 16) = 1 - 0.8413 = 0.1587

So the probability that more than 16 ounces is dispensed in a cup is approximately 0.1587, or about 15.87%.

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The simplest solution for this problem is to traverse the entire array and store the minimum and maximum values.

C++ implementation for the following problem

#include <iostream>

int main(){  

int arr[] = {1,2,3,4,5,6,7,8,9...........................99,100}; //initialize array

int min = arr[0]; //start value

int max= arr[0];  //start value

for(int i:arr) {

 if(i<min) min=i; // if current number lower update min

 if(i>max) max=i; // if current number bigger update max

}

std::cout<<"Min Value: "<<min<<"\nMax Value: "<<max<<"\n";

return 0;

}

The simplest solution for this problem is to traverse the entire array and store the minimum and maximum values.

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The domain and the range of the functions are

Graph 1

This graph follows a sinusoidal pattern, and it has the following highlights:

This means that:

Domain = -∝ < x < ∝

Range = 1 <= y <= 3

Graph 2

This graph follows an absolute value pattern, and it has the following highlights:

This means that:

Domain = -∝ < x < ∝

Range = y >= 0

Graph 3

This graph follows an parabolic pattern, and it has the following highlights:

This means that:

Domain = y >= -2

Range = -∝ < y < ∝

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Answer: C. 2,856

Step-by-step explanation: The formula for volume is V= lwh (length x width x hight). So you'd do 28 x 17 x 6 = 2,856.

TRUE. The ANOVA table from a multiple regression includes the F statistic for assessing overall fit. In this case, the F statistic is 2.83. The F statistic is a ratio of two variances, the between-group variance and the within-group variance.

It is used to test the null hypothesis that all the regression coefficients are equal to zero, which implies that the model does not provide a better fit than the intercept-only model. If the F statistic is larger than the critical value at a chosen significance level, the null hypothesis is rejected, and it can be concluded that the model provides a better fit than the intercept-only model.The F statistic can also be used to compare the fit of two or more models. For example, if we fit two different regression models to the same data, we can compare their F statistics to see which model provides a better fit. However, it is important to note that the F statistic is not always the most appropriate measure of overall fit, and other measures such as adjusted R-squared or AIC may be more informative in some cases.Overall, the F statistic is a useful tool for assessing the overall fit of a multiple regression model and can be used to make comparisons between different models. In this case, the F statistic of 2.83 suggests that the model provides a better fit than the intercept-only model.

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Answer:

The most precise name for quadrilateral ABCD with vertices A(-3, 2), B(-1, 4), C(4, 4), and D(2, 2) is a parallelogram.

To see why, we can use the slope formula to find the slope of each side of the quadrilateral. If opposite sides of a quadrilateral have the same slope, then it is a parallelogram.

Slope of AB: (4 - 2) / (-1 - (-3)) = 2/2 = 1

Slope of CD: (2 - 4) / (2 - 4) = -2/2 = -1

Slope of BC: (4 - 4) / (-1 - 4) = 0/-5 = 0

Slope of AD: (2 - 2) / (-3 - 2) = 0/-5 = 0

We can see that the slopes of AB and CD are equal, and the slopes of BC and AD are equal. Therefore, ABCD is a parallelogram.

While it is also true that the opposite sides of this parallelogram are equal in length, we cannot say that it is a rhombus because the diagonals are not perpendicular. We also cannot say that it is a rectangle because the angles are not all right angles. Therefore, the most precise name for this quadrilateral is a parallelogram.

Step-by-step explanation:

If Joel and Duncan split the 15 ounces of hot chocolate evenly, then they each got half of the container.

To find out how much hot chocolate each boy got, we need to divide the total amount of hot chocolate by the number of people sharing it. Since there are two boys, we can divide 15 by 2 to get the amount of hot chocolate each boy received: 15 ÷ 2 = 7.5

Therefore, each boy got 7.5 ounces of hot chocolate to drink while they went sledding.It's important to note that when dividing something equally between two people, we divide by two since there are two individuals.

In this case, each boy received half of the container, or half of the total amount of hot chocolate. This type of division is known as "fair" or "equal" sharing, as both parties receive an equal portion.

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Answer:

m>=-5

Step-by-step explanation:

-0.5<=m/10

m>=-0.5(10)

m>=-5

Answer: 5

Step-by-step explanation: -4×5=-20

The value of m on solving the equation 6 1/9m+ 3 1/3m = 28 1/3 is 3

We need to solve the equation

6 1/9m+ 3 1/3m = 28 1/3 for m

converting mixed fractions into improper fractions

55/9 m + 10/3 m = 85/3

Upon taking L.C.M.

55/9 m + 10x3/3x3 m = 85/3

(55 + 30)m/9 = 85/3

3 x 85m = 85 x 9

m = 3

Therefore, the value of m on solving the equation 6 1/9m+ 3 1/3m = 28 1/3 is 3

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In a competitive market, we need to graph the market demand and supply curves and determine the equilibrium quantity. The equilibrium quantity represents the quantity at which the demand and supply curves intersect.

To sketch the supply and demand curves, we first need to gather information on the market demand and supply. The demand curve represents the quantity of ventilators that the four hospitals are willing to purchase at different prices, while the supply curve represents the quantity of ventilators that the four producers are willing to sell at different prices.

Using the multipoint drawing tool, we can plot the market demand curve based on the data provided for the hospitals. Label this line as 'Demand'. Next, using the same tool, we can plot the market supply curve based on the data provided for the producers. Label this line as 'Supply'.

The equilibrium quantity is determined at the point where the demand and supply curves intersect. It represents the quantity of ventilators that will be sold in the market. To find this point, we identify the quantity at which the demand and supply curves meet on the graph.

By following the instructions and accurately plotting the demand and supply curves, we can determine the equilibrium quantity of ventilators sold in the market.

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