Create a diagram based on the given symbolic statement. Be sure enough information is provided in the diagram to validate each statement.
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All of the angles in an acute triangle are less than 90 degrees. Triangles are referred to as right triangles when one of their angles is 90 degrees.

The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. 180 degrees is the sum of the triangle's three angles. With three sides and three vertices, triangles are a particular kind of polygon in geometry.

It has three straight sides and is a two-dimensional figure. As a 3-sided polygon, a triangle is included. Three triangle angles added together equal 180 degrees. In one plane, the triangle is contained. When three straight lines cross, a triangle is the result. There are always three sides and three corners to a triangle (angles). A triangle's vertex is the location at which two of its sides meet.

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Macy had 3 appointments.

Logan had 5 appointments.

What is the quadratic equation?

A quadratic equation is a type of polynomial equation of degree 2, which is written in the form of "ax^2 + bx + c = 0", where x is the variable and a, b, and c are constants. The solutions to a quadratic equation can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac))/2a.

Part A:

Let x be the number of appointments Macy had.

We know that the total income (60x + 40) must equal 220.

Therefore, the equation representing the situation is:

60x + 40 = 220

To solve for x, we can subtract 40 from both sides:

60x = 180

Finally, we divide both sides by 60 to get:

x = 3

Macy had 3 appointments.

Part B:

Let y be the number of appointments Logan had.

We know that the total profit (70y + 50 - 20y) must equal 300.

Therefore, the equation representing the situation is:

50y + 50 = 300

To solve for y, we can subtract 50 from both sides:

50y = 250

Finally, we divide both sides by 50 to get:

y = 5

Logan had 5 appointments.

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If the 3 times of total number of adults was 17 less than number of children who visited the petting zoo , then the equation to model this relationship is written as c = 3a + 17   ;

let the number of children in the petting zoo be = c ;

and the number of adults in the petting zoo is = a ;

given that the the number of children are 3 times the number of adults ;

that means ⇒ c = 3a ;

and also given that the difference between the number of children and number of adults is 17 .

This situation can be represented as :

⇒ c - 3a = 17 ;

⇒ c = 3a + 17 .

Therefore , the equation to model this relationship is "c = 3a + 17" .

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Answer:

Part A.) 153 Boxes

Part B.) 394 Boxes (395 if rounding up)

Step-by-step explanation:

The inequality used in this situation would be:

3.74x + 25 < 600

3.74 is the price of each box

x is the number of boxes

25 is that deposit

and < 600 is not making $600 in sales

What we need to do is get X alone. First we will subtract 25 from both sides since that's the opposite of +25.

Doing that will get you

3.74x = 575

Next step is to divide 3.74 on both sides since 3.74 is being multiplied by x and division is the opposite.

That will give you X = 153.74. We round down to stay under and we end up with 153.

For part B, we would do the same process, but instead of < 600, we would do >= 1500. Just typing the same steps out.

3.74x >= 1475 since we subtract 25 from both sides

x = 394.38 since we divide 3.74 on both sides. Rounding would get us 394

The height of the new prism so that its surface area is doubled will be 26.31 cm.

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

A right rectangular prism measures 12 cm tall, 3 cm long, and 10 cm wide. A manufacturer would like to double the surface area of this prism.

Then the height of the new prism so that its surface area is doubled will be given as,

2 x 2 x (12 x 3 + 3 x 10 + 10 x 12) = 2(3h + 3 x 10 + 10h)

2(36 + 30 + 120) = 13h + 30

372 = 13h + 30

13h = 342

h = 26.31 cm

The height of the new prism so that its surface area is doubled will be 26.31 cm.

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The time to calculate her rate along the summit Rate = 1.5 mph

Rate = Distance / Time

To solve this problem, we will first need to calculate the time it took Jane to reach the peak. Since she rode 40 miles uphill, we can use the rate of 5 mph slower than when she reached the peak to calculate this time.

Time = Distance / Rate

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5 mph)

Time = 40 miles / (Rate - 5)

Time = 8 hours

Since Jane spent 2 hours exploring the mountain, the total time it took her to reach the peak was 8 hours. We can now use this time to calculate her rate along the summit.

Rate = Distance / Time

Rate = 12 miles / 8 hours

Rate = 1.5 mph

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Assuming all the workers employed at the beanbag factory are of equal ability, the beanbag factory invest in more equipment to address the diminishing marginal returns it experiences after the hire of its third worker. So the option B is correct.

It is assumed that all of the factory's employed employees have the same level of skill. Additionally, it must follow that if they are working to their maximum ability, they will be able to accomplish the same amount of work as before.

Since the third man was hired, the quantity of work the three of them have completed has decreased, making it clear that he is to blame for the diminishing returns.

Therefore, it seems sense to fire the individual since he is either not performing to his full capacity or encouraging other employees to do the same.

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Starch and protein levels are checked for In order to present the idea of chemical compound variety, it is necessary to test for the presence of starches and protein macromolecules.

Hypothesis: It is a negative result if the biuret reagent remains blue after a test for protein since the reagent itself is blue. The test for protein is positive if a solution is pinkish purple or purple. The starch test solution is a yellowish brown color. We utilized iodine to test for starch in some solutions if any ingredient produced a mixture that was yellowish brown in color. Polysaccharides, monosaccharides, and disaccharides are separated from starch by iodine. Iodine interacts with molecules, changing the color of the molecules, while starch is a coiled polymer of glucose.

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Answer:

1. yes

2. No

Step-by-step explanation:

1. The triangles are congruent

2. It's not matching

Answer:

Step-by-step explanation:

The total percentage increase in the investor's stock account was of 4.55%.

The values of the stocks of Company A and Company B, after the increase are given, respectively, by:

Company A: 3300 x 1.04 = $3432.

Company B: 4140 x 1.05 = $4347.

The total values are given as follows:

Before the increase: 3300  + 4140 = 7440.

After the increase: 3432 + 4347 = 7779.

The percent increase is given by the increase divided by the initial value and multiplied by 100%, hence:

P = (7779 - 7440)/7440 x 100% = 4.55%.

The total percentage increase in the investor's stock account was of 4.55%.

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Step-by-step explanation:

I Don't even know what the answer is

A graph which represent the function g(x) = 3∛x – 1 is: graph A.

In Mathematics, a graph simply refers to a type of chart that is typically used for the graphical representation of ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which indicates the x-axis  and y-axis respectively.

Based on the information about this graph, it represents the following function:

Function, g(x) = 3∛x – 1

By rewriting the cube root in the above function, we have the following:

Function, g(x) = 3∛x – 1

Function, g(x) = 3(x^{1/3}) – 1.

Next, we would use an online graphing calculator to plot the given function as shown in the graph attached below.

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The following two methods can be used for eliminating the damage to the laundry (l).

The factory and the local resident must decide whether to install the scrubber or the clothesline, depending on which option will result in the lowest cost. The best option for each party depends on their own willingness to pay for the damage reduction and their ability to pay for the solution.

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The length of PT is 3 units. The solution has been obtained using the concept of transformation.

What is transformation?

A transformation is an operation that moves a polygon or other two-dimensional object on a plane or coordinate system.

The term "pre-image" or "inverse image" refers to the shape in two dimensions prior to any modification. The image is the shape after transformation.

Transformation can be done by translation, rotation, reflection and dilation.

We are given two rectangles ABCD and PRQT

AB = DC = 3 units

AD = BC = 10 units

It can be observed that the rectangles PRQT and ABCD are same but PRQT is rotated.

Since, they are same so,

AB = PT = 3 units

Hence, the length of PT is 3 units.

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If the growth rate of bacterial culture is 150% each hour , then the correct exponential function is b(t) = 10(2.5)^t instead of b(t) = 10(1.5)^t , and after 8 hours there are about 15259 bacteria in culture .

The percent growth in the bacterial culture is = 150% = 1.5  ;

the initial amount of bacteria present is = 10  ;

the exponential function used to denote this situation is written as :

⇒ b(t) = 10(1 + 1.5)^t

⇒ b(t) = 10(2.5)^t

to find number of bacteria after 8 hours ,

we substitute t = 8 in b(t) ;

we get ;

⇒ b(8) = 10(2.5)⁸ ;

⇒ b(8) = 15258.789 ≈ 15259

Therefore , there will be 15259 bacteria present after 8 hours .

The given question is incomplete , the complete question is

The growth rate of a bacterial culture is 150% each hour. Initially, there are 10 bacteria. Describe the error in the data below, in finding the number of bacteria in the culture after 8 hours. Correct the error and find, to the nearest whole number,

"The number of bacteria in the culture after 8 hours. The exponential function is b(t) = 10(1.5)^t ,  b(8) = 10(1.5)⁸ . After 8 hours, there are about 256 bacteria in the culture ."

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Answer:

I got 0.6

Step-by-step explanation:

plug in c and d

0.5(15) - 2.3(3)

multiply them

7.5 - 6.9 = 0.6

12.2 % of the area painted blue of the figure representing a square with attached triangle on one side with perpendicular height 4cm is equal to 4.27 cm² .

Figure having square attached with triangle on one side.

Side length of the square = 5 cm

Area of the square = ( side-length )²

                                = 5²

                                = 25 cm²

Triangle attached on one side of the square with height = 4cm

Area of the triangle = ( 1/2) × base × height

                                = ( 1/2) × 5 × 4

                                = 10 cm²

Total area of the figure = 25 + 10

                                      = 35 cm²

Percent of area painted blue = 12.2% of total area

                                               = ( 12.2 / 100 ) × 35

                                               = 4.27 cm²

Therefore, for the given figure made up of square and triangle area to be painted blue is equal to 4.27 cm².

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Considering that the leading digit is never zero , then the number of 9 digit integers that can contain exactly 5 zeroes are 367416 numbers   .

the number of digits in the number is = 9 digits ;

the number should have exactly five zeroes  ,

the number of ways to pick five of the digit positions for the zeroes, since the first digit can’t be zero is  = ⁸C₅ ,

There are 9 possible digits for each of other 4 positions as  other positions are occupied by 0 ,

So, the total number of possibilities is = ⁸C₅ × 9⁹⁻⁵

Simplifying further ,

we have ,

= ⁸C₅ × 9⁴

= 56 × 6561

= 367416 numbers .

Therefore , there can be 367416 numbers of 9 digits having 5 zeros .

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Using Quadratic formula, the roots of the equation are -11 + √217/6, -11 - √217/6 .

Equations involving quadratics The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0.

Any quadratic problem can be solved using the quadratic formula. The equation is first changed to have the form ax2+bx+c=0, where a, b, and c are coefficients. After that, we enter these coefficients into the following formula: (-b(b2-4ac))/(2a).

Using Quadratic formula,

3x² + 11x - 8

(-b±√(b²-4ac))/(2a)

⇒ (-11 ± √11² - 4(3)(-8)/2(3))

⇒ -11 ± √217 / 6

⇒ -11 + √217/6, -11 - √217/6

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Answer:

He only accepts jobs that last 4 or more hours.

Step-by-step explanation:

He only accepts jobs that last 4 or more hours.

He only accepts jobs that last 5 or more hours.

He only accepts jobs that last 8 or more hours.

He only accepts jobs that last 9 or more hours.

30 + 15x ≥ 90

15x ≥ 60

x ≥ 4

Answer: He only accepts jobs that last 4 or more hours.

The lateral surface area of the cylinder is 51.22 cm2.
What is surface area?
Surface area is a two-dimensional measure that refers to the total area of a surface, such as the area of a two-dimensional shape, a three-dimensional solid, or a combination of both. It is the sum of the areas of all the faces of a solid object. It is also referred to as the area of the boundary of a three-dimensional object. It can be used to calculate the volume of an object, and is also used in other calculations like area of the base of a triangle, area of a circle, and more.

The cylinder shown below has a diameter of 5.2 cm on the base and a height of 7.1 cm. The diameter of the base is referred to as 'd' and the height of the cylinder is referred to as 'h'. The lateral surface area of the cylinder can be found by using the formula LSA = 2πrh, where 'r' is the radius of the base. The radius of the base of this cylinder is half of the diameter, or 2.6 cm. Therefore, the lateral surface area of the cylinder is: 2π x 2.6 x 7.1 = 51.22 cm2.

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As per the given parentage, the highest percentage saying the greens are too fast is females.

In math the term percentage is defined as the number or ratio that can be expressed as a fraction of 100.

Here we have know that the number male players are

Male Golfers                                    Greens Condition              

Handicap                               Too fast                        Fine

Under 15                                       10                             40

15 or more                                     25                           25

And the female players are,

Male Golfers                                     Greens Condition            

Handicap                               Too fast                         Fine

Under 15                                       1                                9

15 or more                                   39                              51

Then the total value of them is calculated as,

                      Too fast                   Fine             Total

Male                   35                          65               100

Female              40                           60               100

So, the group with the highest percentage of too fast is the females.

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The best statistical test to be used is multiple linear regression analysis.

Multiple linear regression is a statistical method that allows you to examine the relationship between two or more independent variables (in this case, level of education, gender, and annual income of the student's parents) and one dependent variable (annual income and student loan debt).

It will help you determine how much of the variation in the dependent variable is explained by the independent variables, and the strength and direction of the relationships between the variables.

In this case, this test will allow us to determine the impact of a student's level of education, gender, and the annual income of their parents on their annual income and student loan debt while accounting for the possible confounding effect of the annual income of their parents on these variables.

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True, free bilirubin is transported by the blood to the liver.

Macrophages begin the disposal of hemoglobin by separating the heme from the globin. They hydrolyze the globin into free amino acids, which can be used for energy-releasing catabolism or recycled for protein synthesis.

Bilirubin

Bilirubin is a red-orange compound that occurs in the normal catabolic pathway that breaks down heme in vertebrates. This catabolism is a necessary process in the body's clearance of waste products that arise from the destruction of aged or abnormal red blood cells.

Hemoglobin

Hemoglobin is a protein in your red blood cells that carries oxygen to your body's organs and tissues and transports carbon dioxide from your organs and tissues back to your lungs.

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The values of x from the given figures are 3 √29 and 24 respectively.

What is triangle ?

Triangle can be defined in which it has three sides , three angles and sum of three angles is always 180 degrees.

Given

In the figure,

The two given triangles are similar ,

So, in the first figure it is given that they are similar ,

√29 / 5  = x / 15

x  = √29 * 15  / 5

x =√29 * 3

x = 3 √29

And in the second figure , here also they gave they are similar

so we get,

12 / 13  =  x /  26

x = 12 * 26 / 13

x = 12 * 2

x = 24

Hence, The values of x from the given similar triangles are 3 √29 and 24 respectively.

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For the given function H(t) = -12cos( πt/45 ) + 18 the maximum height is  30 units.

Function to modeled the height 'H' of the Ferries wheel is given by:

H(t) = -12cos( πt/45 ) + 18

Where 't' represents the time in seconds.

For cosine trigonometric function,

-1 ≤ cosα ≤ 1

Here cos function lies between two values -1 and 1.

Substitute cos( πt/45 ) = 1 or -1

When cos( πt/45 ) = 1

H(t) = -12(1) + 18

⇒H(t) = 6 units

When cos( πt/45 ) = -1

H(t) = -12(-1) + 18

⇒H(t) = 30 units

Maximum height of a required cabin is equals to 30 units.

Therefore, the maximum height of given cabin represented by the function

H(t) = -12cos( πt/45 ) + 18 is equal to 30 units.

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The  value for n that would make the inequality true is 4.5

You should understand that a statement of an order relationship with greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions is inequality.

The given inequality is ⁿ⁄₉ > ½

This implies that 2(n) > 1(9)

Opening the brackets to have

2n > 9

Making n the subject of the relation by dividing both sides by 2

2n/2 > 9/2

Therefore n = 4.5

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The total cost of 6 apples and 3 oranges is $6 + $6 = $12.

The total cost of 4 apples and 4 oranges is $4 + $8 = $12.

The total cost of 5 apples and 4 oranges is $5 + $8 = $13.

The total cost of 8 apples and 2 oranges is $8 + $4 = $12.

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The remaining rope he left is 495cm

Now, According to the question:

Multiplication is an operation that represents the basic idea of repeated addition of the same number. The numbers that are multiplied are called the factors and the result that is obtained after the multiplication of two or more numbers is known as the product of those numbers.

Jacob has 6. 15 meters of rope.

He is going to use 1. 2 meters of rope to tie up his boat.

When you do the subtraction, whatever is left (the decimal part) is the length in cm when multiplied by 100.

Remaining rope = starting length - what was used.

Remaining rope = 6.15 - 1.2

Remaining rope = 4.95 meters

Hence, The remaining rope he left  = 4.95 × 100 = 495 cm

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