Mark is doing a course.There are 5 tests on the course. He needs a mean score of 10 to pass. In his first 4 tests his mean score is 12. What score does he need in the 5th test to pass the course

The scale factor of the dilation will be 1/4.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The blue figure is a dilation image of the black figure.

And, The origin is the center of dilation.

Now,

Since, The blue figure is a dilation image of the black figure.

And, The origin is the center of dilation.

Here, The length of black figure = 8 units

And, The length of blue figure = 2 units

So, The scale factor of the dilation = 2/8

                                                         = 1/4

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[tex]\textit{circumference of a circle}\\\\ C=2\pi r ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ C=23\pi \end{cases}\implies 23\pi =2\pi r\implies \cfrac{23\pi }{2\pi }=r\implies \cfrac{23}{2}=r \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{23}{2} \end{cases}\implies A=\pi \left( \cfrac{23}{2} \right)^2\implies A=132.25\pi[/tex]

Step-by-step explanation:

First, we need to perform the multiplication operation within the parentheses, following the order of operations:

2⅓ × 1¼ = (7/3) × (5/4) = 35/12

Now, we can substitute the values in the expression:

3½ - (2⅓ × 1¼) + ⅗ = 7/2 - 35/12 + 3/5

To add or subtract fractions with different denominators, we need to find a common denominator. The least common multiple of 2, 12, and 5 is 60, so we can rewrite the fractions with this denominator:

7/2 - 35/12 + 3/5 = (210/60) / (2/2) - (175/60) / (12/12) + (36/60) / (5/5)

Simplifying the fractions within the parentheses:

= 210/60 - 175/60 + 36/60

= 71/60

Therefore, 3½ - (2⅓ × 1¼) + ⅗ simplifies to 71/60.

The figure has rotational symmetry of order 2 and to achieve rotational symmetry of order 4, three plates need to added.

Explain about symmetry?

Symmetry is a property of an object that describes how it appears identical after some transformation, such as reflection, rotation, or translation. It is an essential concept in mathematics, science, art, and many other fields.

There are several types of symmetry, including:

Reflectional symmetry (also called bilateral symmetry).
Rotational symmetry.

Translational symmetry.

According to the question:

a. The figure has rotational symmetry of order 2. This means that if we rotate the figure 180 degrees around its center, the figure will look exactly the same as it did before the rotation.

b. To achieve rotational symmetry of order 4, we need to add plates in such a way that the figure looks the same after a rotation of 90 degrees, 180 degrees, and 270 degrees around its center.
To achieve this, we can add three more plates to the figure, one in between each pair of existing plates, After adding these plates, the figure has rotational symmetry of order 4. We can see this by rotating the figure 90 degrees, 180 degrees, and 270 degrees around its center

so the figure has rotational symmetry of order 4. Therefore, we only needed to add three plates to the figure to achieve rotational symmetry of order 4 around its center.

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The savings plan balance after 2 years with an APR of 6% and monthly payments of $150 is approximately $3,814.79.

What are payments?

In compensation for products or services received or to fulfill a legal duty, payment is the voluntarily given exchange of money, its equivalent, or other valuables from one person to another. Frequently, the individual giving the money is referred to as the payer, while the person receiving it is referred to as the payee.

Assuming that the payments are made at the end of each month, we can use the formula -

[tex]A = PMT\Bigg[\frac{\big(1+\frac{APR}{n}\big)^{nY}-1}{\frac{APR}{n}}\Bigg][/tex]

where -

A = the savings plan balance after 2 years

PMT = the monthly payment ($150)

APR = the annual percentage rate (6%)

n = the number of compounding periods per year (12, since the payments are made monthly)

Y = the number of years (2)

Plugging in the values, we get -

[tex]A = 150\Bigg[\frac{\big(1+\frac{0.06}{12}\big)^{12 \times 2}-1}{\frac{0.06}{12}}\Bigg][/tex]

A ≈ $3,814.79

Therefore, value is obtained as $3,814.79.

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The correct inequality that represents the allowable measurements the bar can bend is | x - 4.5 | ≤ 0.1 , So correct option is E.

n mathematics, an inequality is a statement that indicates that two values are not equal. It is a relationship between two expressions that can be compared using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

For example, 5 < 10 is an inequality that indicates that 5 is less than 10. Similarly, x + 3 ≤ 8 is an inequality that indicates that the sum of x and 3 is less than or equal to 8.

Inequalities are used to express relationships between quantities that are not necessarily equal. They can be used to represent constraints, limits, or ranges of values. Inequality statements can be combined with other mathematical expressions, such as equations or inequalities, to create more complex mathematical models.

The correct inequality that represents the allowable measurements the bar can bend is:

| x - 4.5 | ≤ 0.1

This is because the average allowable bend is 4.5 cm with a margin of error of 0.1 cm, which means that the actual allowable bend can range from 4.4 cm to 4.6 cm. The absolute value inequality represents this range of values, with the center of the range being 4.5 cm.

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Therefore, if a population of 150 mice triples in size every four months, there will be approximately 2,952,450 mice in the neighbourhood in 3 years.

Mathematicians use the unitary method to answer proportional relationship problems involving two or more quantities. It entails calculating the worth of one unit of one quantity in relation to another. For instance, let's say we are aware that 3 pencils cost $6. The following is how we can calculate the price of a solitary pen using the unitary method: The value of a single entity of the quantity "pen cost" in terms of the quantity "number of pens" was determined in this case. Once we are aware of a unit's worth, we can use that knowledge to determine the value of any other quantity that is related to it.

given

The population triples, or grows three times, in number, after four months. As a result, if we commence with 150 mice, the population will look like this after 4 months:

150 × 3 = 450 mice

The populace will triple once more after another 4 months (or 8 months from the beginning), becoming:

450 × 3 = 1350 mice

The populace will triple once more after another 4 months (or 12 months from the beginning), becoming:

1350 × 3 = 4050 mice

There is a pattern here: every four months, the populace triples. Therefore, we can determine how many times the population triples after three years (or 36 months) have passed:

36 months divided by 4 months per triple equals 9 triples.

the following group will exist after three years:

2,952,450 mice are equal to 150 × 39 (150 x 19,683).

Therefore, if a population of 150 mice triples in size every four months, there will be approximately 2,952,450 mice in the neighbourhood in 3 years.

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The final answer is 1/10, which is a reduced fraction in lowest terms.

What is the fraction?

A fraction is a mathematical expression that represents a part of a whole or a division of one quantity by another.

To perform the operation described, we first need to multiply the two fractions together using cross multiplication:

(3/5) x (1/6) = (3 x 1) / (5 x 6) = 3/30

The resulting fraction 3/30 is an improper fraction, meaning that the numerator is larger than the denominator. To convert this to a mixed fraction, we need to divide the numerator by the denominator, and express the remainder as a fraction. In this case:

3/30 = 1/10

Hence, the final answer is 1/10, which is a reduced fraction in lowest terms.

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The expression [tex]\frac{3x^2 + 6x + 3}{x + 1}[/tex] , where x ≠ -1, is equivalent to Option (D) 3x + 3. We can factor the numerator of the expression by first factoring out the greatest common factor of 3.

What is numerator ?

In a fraction, the numerator is the top number that represents the quantity being considered.

Take 3 common from expression:

[tex]3(x^2 + 2x + 1)[/tex]

We can further factor the expression inside the parentheses using the identity [tex](x + 1)^2 = x^2 + 2x + 1[/tex] , giving:

[tex]3(x + 1)^2[/tex]

Therefore, the original expression can be written as:

[tex]\frac{3(x + 1)^2}{x + 1}[/tex]

We can simplify this expression by canceling out the (x + 1) term in the numerator and denominator, leaving us with:

[tex]3(x + 1)[/tex]

So the expression [tex]\frac{3x^2 + 6x + 3}{x + 1}[/tex] , where x ≠ -1, is equivalent to 3(x + 1). This expression represents a straight line with a slope of 3 and a y-intercept of 3.

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The value of x is given as follows:

x = 4.8.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

In the context of this problem, the parameters are given as follows:

Applying the Pythagorean Theorem, the value of x is obtained as follows:

x² + 14² = (x + 10)²

x² + 196 = x² + 20x + 100

20x = 96

x = 96/20

x = 4.8.

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One mistake Quinn made was in setting up the equation.

An equation is a mathematical statement that expresses the relationship between two or more quantities, using symbols such as +, -, =, and so on. It can be used to solve problems involving unknowns, such as the number of solutions to an equation or the value of a certain variable. In addition, equations can help to predict future outcomes based on current data.

Quinn set up the equation incorrectly by subtracting 3/2 from both sides instead of subtracting 3/1 from both sides. This caused the equation to become unbalanced, resulting in an incorrect solution. To solve the equation correctly, Quinn should have subtracted 3/1 from both sides to get the correct equation: 2/3 = q.

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she made the mistake of calculating

Step-by-step explanation:

The inverse of the function will be f⁻¹(y) = y + 1.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.

The given function is y = x - 1.

To find the inverse of this function, we need to solve for x in terms of y.

y = x - 1

Adding 1 to both sides, we get:

y + 1 = x

Therefore, the inverse function is:

x = y + 1

f⁻¹(y) = y + 1

Note that the inverse function represents the reflection of the original function across the line y = x.

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The equation for number of miles is 14/7 = x and she ran 2 miles each day.

Simplify the equation to bring all the variable terms to one side and the constant value to the other in order to solve linear equations with a single variable. Find the LCM (least common multiple) if there are any fractional terms, then simplify them so that the variable values are on one line and the steady terms are on the other.

Let us suppose the number of miles she ran each day = x.

Given that, Aroline ran 14 miles in 7 days.

Thus,

Total distance / Number of days = x

14/7 = x

x = 2

Hence, the equation is 14/7 = x and she ran 2 miles each day.

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Answer:

The correct answer you're looking for is either 85, or 68.07 (rounded)
The correct answer is if x is the hypotenuse or the most extensive length than its 85.
If x is one of the legs then 68.07 (rounded) is the correct answer.

Recommendation:

When trying to solve for a missing length you need to be sure whether it's just a leg or the hypotenuse, usually would be obvious in a picture as the sides attached to the 90º angle are usually legs and the one opposite of it is the hypotenuse.
Anywho below are the two different ways to get the answer.

Disclaimer:

There will be two answers that I will have given and I would suggest looking at the question to see which one it is, I am not only giving one possible answer. (Also very long answer, sorry!)

Note:

If messaged or commented on which numbers go on which side I'll be more than happy to confirm one answer.

Step-by-step explanation:

Figuring out only if X is Hypotenuse:

To solve for a hypotenuse you need to use the equation for the Pythagorean Theorem which states: [tex]a^{2} +b^{2}= c^{2}[/tex].

In this case, 36, and 77 are the two legs that make up this triangle.

We would insert these two numbers to replace a and b for when solving the equation.

Now you have [tex]36^{2}+ 77^{2}= c^{2}[/tex].

You then do the exponent operations for the terms that we know the values of and also add them up together to get this equation:
1296 + 5929 = 7725 or [tex]c^{2}[/tex].

After that, we'll make sure to add the terms on the first side and keep [tex]c^{2}[/tex] on the other and to also square root them giving this equation: [tex]\sqrt{7725} = \sqrt{c^{2}[/tex].

With that, your answer is 85 = X


Figuring out only if X is a Leg:

Figuring out only if X is Hypotenuse:
To solve for a leg you need to use the equation for the Pythagorean Theorem which states: [tex]c^{2}- b^{2}= a^{2}[/tex]

In this case, 36, is one of the two legs that make up this triangle while 77 is the Hypotenuse.

We would insert these two numbers to replace b and c when solving the equation.

Now you have [tex]72^{2} -36^{2} =a^{2}[/tex]

You then do the exponent operations for the terms that we know the values of and also add them up together to get this equation:
5929 - 1296 = 4633 or [tex]a^{2}[/tex]

After that, we'll make sure to subtract the terms on the first side and keep [tex]a^{2}[/tex] them on the other and also to square root them giving this equation:  
[tex]\sqrt{4633} =\sqrt{a^{2} }[/tex]

With that, your answer is 68.07 (rounded) = X

I hope this was helpful!

Out of the fifty people surveyed, thirty prefer vanilla frozen yogurt. The circle graph is a useful visual representation of the survey results.

A circle graph, also known as a pie chart, is a type of graph that displays data in a circular format. It is divided into sections that each represent a proportion of the whole. The sections are labeled and the relative sizes of each section show the proportion of the whole that each part represents.

The circle graph indicates that 30 people prefer vanilla flavor. This is the highest amount out of the five flavors represented. The graph shows that the next most popular flavor is chocolate, preferred by 20 people, followed by strawberry, preferred by 10 people. There are five people who prefer a different flavor, and five people who have no preference. Therefore, out of the fifty people surveyed, thirty prefer vanilla frozen yogurt.

The circle graph is a useful visual representation of the survey results. By looking at the graph, it is clear that vanilla is the most popular flavor, with thirty people preferring it.

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Answer:

I speak english so this might be wrong...

Step-by-step explanation:

Build the distribution table

of frequencies and histogram of the height (in cm) of 80 third-secondary students.

(Construir la tabla de distribución

de frecuencias e histograma de la altura (en cm) de 80 estudiantes de tercero medio.)

I think this is what you sayed?

For the following:

a) To determine the range of the heights, find the difference between the highest and lowest values.

Range = Highest value - Lowest value

The highest value is 188 cm, and the lowest value is 162 cm.

Range = 188 - 162 = 26 cm

b) The amplitude is the interval width of each class in the frequency table. To determine the amplitude, Know the number of classes. Assume to create 10 classes for the height data.

Amplitude = Range / Number of classes

Amplitude = 26 cm / 10 = 2.6 cm

c) To build the frequency table, to create the class intervals for the height data. Since the amplitude is 2.6 cm, choose the class intervals accordingly.

Set up the frequency table with 10 classes:

Class Intervals: (160 - 162.6], (162.6 - 165.2], (165.2 - 167.8], ..., (185 - 187.6], (187.6 - 190]

Next, count the number of data points falling into each class interval and calculate the absolute frequency (frequency), cumulative frequency, relative frequency, and percentage relative frequency.

The frequency table for the height data is attached.

In the frequency table, the "Cumulative Frequency" column shows the running total of frequencies, the "Relative Frequency" column shows the proportion of each class frequency to the total number of data points (80), and the "Percentage Relative Frequency" column shows the relative frequency expressed as a percentage.

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The graph below shows a parabola, indicating that the possible function for f is a quadratic equation.

Graph is a data structure consisting of nodes (vertices) and edges that connect them. Graphs are used to represent networks of data, such as social or computer networks. Graphs are also used to represent mathematical and logical equations, as well as to store and display data. Graphs are composed of two basic components: nodes (vertices) and edges (arcs). Nodes represent the objects in the network, while edges represent the connections between them. Graphs can be used to model many different types of relationships and can be used to solve a variety of problems in different areas, such as computer science, mathematics, engineering, and social sciences.

A quadratic equation is an equation of the form ax2 + bx + c = 0, where a, b and c are real numbers and a ≠ 0. This type of equation is important in mathematics, as it can represent many physical situations, such as a ball thrown into the air, or a spring that is stretched or compressed. Quadratic equations can be solved using the quadratic formula, which uses the coefficients a, b and c to calculate the two solutions for x. In the graph, the parabola has an equation of the form y = ax2 + bx + c, and so the possible function for f is a quadratic equation.

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2k + 5 = 2(8) + 5 = 16 + 5 = 21

k is substituted into the expression

The value of (AB)² + (BC)² = 130

The value of (AC)² = 130.

Therefore the triangle is a right angled triangle

Distance between two points is the length of the line segment that connects the two points in a plane. The formula to find the distance between the two points is usually given by d=√((x2 – x1)² + (y2 – y1)²).

AB)² = 5-(-2)²+7-11)²

= 7² + 4²

= 49+16

AB)² = 65

BC)² = 1-5)² + 0-7)²

BC)² = 4² + 7²

= 16 +49

BC) ² = 65

BC)² + AB)² = 65+65 = 130

AC)² = 1-(-2)² +0-11)²

AC)² = 3²+ 11²

AC)² = 9+121

AC)² = 130

therefore the value of BC)² + AB)² = AC)²

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The proof that proves the two triangles are congruent by the AAS congruence theorem is shown below.

Angle-Angle-Side (AAS) is an abbreviation that refers to a method of determining congruence in triangles. If two triangles have two corresponding angles that are equal, and the non-included side between these angles is also equal, then the triangles are considered congruent.

The proof below shows how to apply the AAS congruence theorem to prove both triangles are congruent.

Statement                           Reason                                  

1. ∠B ≅ ∠D; BC║AD           1. Given

2. AC ≅ CA                         2. Reflexive property

3. ∠BCA ≅ ∠DAC               3. Alternate interior angles theorem

4. △ABC ≅ △CDA              4. AAS congruence theorem

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The triangle can be classified as follows:

NUMBER 4: obtuse

NUMBER 5: obtuse

NUMBER 6: obtuse

NUMBER 7: right

NUMBER 8: right

NUMBER 9: acute

NUMBER 10: right

To classify the triangle as Right, Obtuse, or Acute, follow the following steps:

1. Calculate the sum of squares of the two smaller sides.

2. Compare it to the square of the longest side.

3. If the sum is greater, your triangle is acute. If they are equal, your triangle is right. If the sum is less, your triangle is obtuse.

NUMBER 4

6² + 7² = 58

9² = 81

58 < 81 (obtuse)

NUMBER 5

10² + 12² = 244

16² = 256

244 < 256 (obtuse)

NUMBER 6

8² + 16² = 320

(8√6)² = 384

320 < 384 (obtuse)

NUMBER 7

20² + 21² = 841

29² = 841

841 = 841 (right)

NUMBER 8

8² + 3² = 73

(√73)² = 73

73 = 73 (right)

NUMBER 9

8² + 10² = 164

12² = 144

164 > 144 (acute)

NUMBER 10

9² + 15² = 306

(3√34)² = 306

306 = 36 (right)

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The probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as 0.5.

The probability of an event is a number that indicates how likely the event is to occur.

It is expressed as a number in the range from 0 and 1 or it can be expressed using percentage notation, in the range from 0% to 100%

Given is that the probability of a randomely selected fertilized egg will take 21 days to hatch is 0.028.

We can write the probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as -

P{E} = {0.028 + (1 - 0.028)}/2

P{E} =  1/2

P{E} = 0.5

Therefore, the probability that the randomely selected fertilized egg will hatch between 15 days to 17 days as 0.5.

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Answer:

The given equation is of the form:

((x - h)^2)/a^2 - ((y - k)^2)/b^2 = 1

Comparing it with the given equation:

((x - 3)^2)/10 - ((y + 5)^2)/9 = 4

We can rewrite the equation in the standard form by dividing both sides by 4, then adding (y+5)^2/9 to both sides:

((x - 3)^2)/40 - ((y + 5)^2)/36 = 1

Now, we can see that the equation is in the standard form of a hyperbola. The center of the hyperbola is (3, -5), the distance between the center and each vertex is sqrt(10) in the x-direction and sqrt(9) in the y-direction, and the hyperbola opens to the left and right.

Answer:

32 ft

Step-by-step explanation:

pls make me brainleist

Answer:

Below

Step-by-step explanation:

The wedge shaped area is ABOVE (greater than)  and INCLUDES  y = 5x+2    AND  ABOVE (greater than ) y= -3x-2

See image below:

The result is a statistic because it describes some characteristic of a sample (the 60 states).

what is statistics?

Statistics is the study of collecting, analyzing, and interpreting numerical data to make inferences and decisions. It involves techniques such as sampling, probability, hypothesis testing, and regression analysis to extract meaningful insights from data and make informed decisions based on them.

Solution:

The result is a statistic because it describes some characteristic of a sample (the 60 states).

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The equation of the line that represents the total cost is c = 4d + 8 and the total cost when 1 drink is bought is $ 12.

The slope-intercept form of a line has used to form a linear equation in two variables. It is called the slope-intercept form because it gives us two pieces of information about the line its slope and y-intercept.

The slope-intercept form of a line is given by the equation:

where:

m is the slope of the line

b is the y-intercept of the line

Here we have

The graph shows the total cost c of buying one large bucket of popcorn and d large drinks.  

From the graph, the line passes through points (0, 8) and (1, 12)  

Hence, slope of the line (m) = [(y₂ - y₁) / (x₂ - x₁) ]

= [(12 - 8) / (1 - 0) ] = [4 / 1] = 4

Let y = mx + c be the lines

=> y = 4x + c

Since the line passes through (0, 8)

=> 8 = 4(0) + c

=> c = 8

Hence, the required equation is y = 4x + 8  

From the data,

The y-axis represents the total cost 'c' and the x-axis represents the number of drinks 'd'

=>  Total cost c = 4d + 8

Hence,

The equation of the line that represents the total cost is c = 4d + 8

If we bought 1 large drink

=> c = 4(1) + 8 = 12

Therefore,

The equation of the line that represents the total cost is c = 4d + 8 and the total cost when 1 drink is bought is $ 12.

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