Joel increases his baseball card collection by 2/3 when he purchases 14 more cards. Which expression represents the number of cards he started with?

Answer:

28

Step-by-step explanation:

4 cubed means 4 x 4 x 4, which is 64.

6 squared means 6 x 6, which is 36.

So,

4 cubed - 6 squared = 64 - 36 = 28.

The probability that s student will passed exactly one of the subject is 28/55.

It should be noted that probability simply means the likelihood that a particular event will happen.

Based on the Venn diagram that's given, the number if students that passed both subjects is 19.

Therefore, the probability that s student will passed exactly one of the subject will be:

= Fraction of students that passed French + Those that passes German

= 11/55 + 17/55

= 28/55

The probability is 28/55.

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Answer:

4.The product is greater that 3/8 and less than 7/2.

Step-by-step explanation:

The product of 3/8 and 7/2 is:

\(\frac{3}{8} * \frac{7}{2} \\\\= \frac{21}{16} = 1\frac{5}{16}\)

This number is greater than 3/8.

It is greater than 1/8 but not less than 1/2.

This number is less than 7/2.

This number is greater than 3/8 and it is less than 7/2.

Hence, the correct options is 4.

Answer:

$1505

Step-by-step explanation:

area = 5 x 7 = 35 m²

35 m² x $43 per m² = $1505

One and only one of the two rays issuing from point P either contains ray R or is contained in ray R, as there cannot exist a point Q on one of the rays that lies outside the region defined by R .

To prove that one and only one of the two rays issuing from point P either contains ray R or is contained in ray R, we can use a proof by contradiction.

Assume that both rays issuing from point P do not satisfy the condition, meaning neither contains R nor is contained in R. This implies that there must be a point Q on one of the rays issuing from P that lies outside the region defined by R.

Let's consider the case where point Q lies on the ray issued from P that does not contain R. Since Q is outside the region defined by R, there must be a point S on R such that Q lies between points P and S on line AP.

Now, let's consider the segment AS. Since S lies on ray R, by definition, the segment AS lies completely within ray R. However, since Q lies between P and S, point Q must also lie on segment AS. This means that Q lies within both ray R and outside ray R, which is a contradiction.

Hence, our assumption that both rays issuing from P do not satisfy the condition is false. Therefore, there exists one and only one of the two rays issuing from point P that either contains R or is contained in R.

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The values of the Boolean variable x that satisfy the given equations are x = 1 for equation (a), and there are no solutions for equations (b), (c), and (d).

To answer this question, we need to understand the basics of Boolean variables and equations.

Boolean variables can only have two possible values, either true (represented by 1) or false (represented by 0). Boolean equations are expressions that involve these variables and logical operators such as AND, OR, and NOT.

Now let's look at the given equations and find the values of the Boolean variable x that satisfy them:

a) x = 1: This equation means that the value of x must be 1. So the only solution is x = 1.

b) There are no solutions: This means that there is no value of x that can satisfy this equation.

c) There are no solutions: Similar to the previous equation, there is no value of x that can satisfy this equation.

d) There are no solutions: Again, there is no value of x that can satisfy this equation.

In conclusion, the values of the Boolean variable x that satisfy the given equations are: x = 1 for equation (a), and there are no solutions for equations (b), (c), and (d).

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Answer:

254 in the first blank

Step-by-step explanation:

There are actually 254 counties, The amount of error in Pedro's estimate is 4 and percent error: 1.574%

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part.

Given that

There are 254 counties in the state of Texas. Pedro says that there are about 250 counties in the state.

There are actually 254 counties.

The amount of error in Pedro's estimate is 4.

Now we need to find percent error in Pedro's estimate.

4/254×100

=0.0157×100

=1.574%

Hence There are actually 254 counties, The amount of error in Pedro's estimate is 4 and percent error: 1.574%

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Answer:

Try using a website calculator, or just try and ask a parent guardian for help

From the triangle, the values of a and b are 5.1 units and 4.4 units respectively

You should know that a triangle is a polygon with three sides, three vertices, three angles  whose sum of angles is 180⁰

Using the trig ratio of Cosine

CosY=Adjacent/Hypothenuse

cos31=w/6

Cross multiplying we have

6*cos31=w

w=5.1 units

Then to find b, note that /VW/=/VY/=5.1

<VYX=<VWX............... base angles of isosceles triangle  WVY

Using cosine again from trig.

Cos31=b/5.1

5.1*cos31=b

simplify to get b=4.4 units

Therefore b= 4.4 units  

a=90-31       (remaining 2 angles of a right angled triangle)

a=59⁰

In conclusion, the value of a=59⁰ and the value of b=4.4 units

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Answer:

B

Step-by-step explanation:

The triangle RUS is similar to RST. 9/sqrt(90)=y/(3+x) and y^2=x^2+81. Solving all this will give x=27 and y=9*sqrt(10)

Value of x is 27 and value of y is \(9\sqrt{10}\).

The angle addition postulate in geometry states that if we place two or more angles side by side such that they share a common vertex and a common arm between each pair of angles, then the sum of those angles will be equal to the total sum of the resulting angle.

X-value:

<RST = \(90^{0}\)

\(tan( < RSU)= \frac{\overline R \overline U}{\overline S \overline U}\)

\(tan( < RSU) = \frac{3}{9}\)

\(< RSU = 18.435^{0}\)

Angle addition postulate:

<RST = <RSU + <TSU

\(90^{0} =18.435^{0} + < TSU\)

\(< TSU =71.565^{0}\)

\(tan( < TSU) = \frac{\overline T \overline U }{\overline S \overline U}\)

\(tan(71.565^{0})=\frac{x}{9}\)

\(x=27\)

Y-value:

<RST = \(90^{0}\)

\(tan( < RSU)= \frac{\overline R \overline U}{\overline S \overline U}\)

\(tan( < RSU) = \frac{3}{9}\)

\(< RSU = 18.435^{0}\)

Angle addition postulate:

<RST = <RSU + <TSU

\(90^{0} =18.435^{0} + < TSU\)

\(< TSU =71.565^{0}\)

\(cos( < TSU) = \frac{\overline S \overline U }{\overline S \overline T}\)

\(cos(71.565^{0})=\frac{9}{y}\)

\(y=9\sqrt{10}\)

Value of x is 27 and value of y is \(9\sqrt{10}\).

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in case of box start being tilt,

box should be half out the table,

The Center of Mass of an object or system of objects is a location that is specified in relation to those objects. The Center of Mass of a system is the location where all of its components are on average when they are all weighted in accordance with their masses. The centroid is where basic stiff objects with homogenous density have their centers of mass. Sometimes an object's Center of Mass might not be directly over it. The Center of Mass would be on the Center in the event of a uniform disc, but there would be no material in the case of a ring where the Center of Mass would be on the Center.

The Centre of Mass for intrinsic shapes can be defined as the position where the sum of all of its weighted position vectors of all the parts equals zero.

In this we can use the Center of Mass concept,

As it will leave table when normal is not acting from the table at the center of mass.

So, as in case of box measuring ( x, y, z ) the center of mass from any point of the box is \(\sqrt{x^{2} +y^{2}+ z^{2} }\)

So in case of box start being tilt,

box should be half out the table,

So that COM must be just outside the table

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Answer:

6 sqrt(3) = x

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/ hyp

sin 60 = x/12

12 sin 60 =x

12 ( sqrt(3)/2) =x

6 sqrt(3) = x

Answer:

x=6\(\sqrt{3}\)

Step-by-step explanation:

take 60 degree as reference angle

using sin rule

sin 60=opposite/hypotenuse

\(\sqrt{3\)/2=x/12

do cross multiplication

2*x=12*\(\sqrt{3}\)

x=12\(\sqrt{3}\) /2

x=6\(\sqrt{3}\)

(10x-3=15x-18)

X = -1

Hey there!

\(Answer:\boxed{x=-1}\)

\(Explanation:\)

10x - 3 = -5x - 18

10x - 3 + 5x = -5x - 18 + 5x      Add 5x to both sides

15 - 3 = -18

15x - 3 + 3 = -18 + 3    Add 3 to both sides

15x = -15

15x/15 = -15/15

x = -1

Hope this helps!

Answer:

The area of the shape is 84cm squared.

Step-by-step explanation:

-The area for a rectangle is A=l*w.

-The area for a triangle is 1/2*b*w.

-The area for the rectangle is 12cm*6cm=72cm.

-The area for the triangle is 1/2*8cm*3cm=12cm.

-Now you add 72cm+12cm=84cm.

Do not forget:

You must add the small 2 or put squared because it is a 2D figure.

Answer:

2 nonreal solutions

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 (a ≠ 0 )

then the nature of the roots are determined by the discriminant

b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational solutions

• if b² - 4ac > 0 and a perfect square then 2 real and rational solutions

• if b² - 4ac = 0 then 2 real and equal solutions

• if b² - 4ac < 0 then no real solutions

5x² - 2x + 6 = 0 ← in standard form

with a = 5 , b = - 2 , c = 6

b² - 4ac

= (- 2)² - (4 × 5 × 6)

= 4 - 120

= - 116

since b² - 4ac < 0

then there are 2 nonreal solutions to the equation

Answer:

First, you get both of them with same denominator:

3/7 and 2/3 => 9/21 and 14/21, however, there are only 4 rational numbers between 9/21 and 14/21.

The solution is that you can raise the denominator 2 times:

9/21 and 14/21 => 18/42 and 28/42

Now you can select : 19/42, 20/42, 21/42, 22/42, 23/42. They are a group of  5 rational numbers you are looking for.

The answer to question is given briefly

a) Clearly state the null and alternative hypotheses

In this scenario, we are required to check whether the proportion of people taking a vitamin pill regularly is different from 35%.

The null hypothesis, H0:

The proportion taking a vitamin pill regularly is 35%.

The alternative hypothesis, H1:

The proportion taking a vitamin pill regularly is not equal to 35%.

b) Calculate the test statistic and p-value.

To find the test statistic and p-value, we'll need to perform a hypothesis test. Using the binomial distribution, we can easily determine this.

Binomial probability distribution is used in this scenario to check the data provide evidence that the proportion taking a vitamin pill regularly is different from 35%.

Here, the sample proportion can be calculated as, sample proportion, p = (no. of people taking a vitamin pill regularly) / (total no. of people) = 98/315=0.311

In the binomial distribution, the formula for calculating the test statistic z can be given as,

z = (p - P) / √(P(1 - P)/n)

where p is the sample proportion, P is the hypothesized proportion, and n is the sample size.

Using this formula, we have;

z = (0.311 - 0.35) / √(0.35(1 - 0.35)/315)=-1.89

The calculated test statistic, z = -1.89

Using the z-score table, we can find the p-value. The p-value corresponding to a z-score of -1.89 is 0.0594.

c) Can we conclude that the proportion taking a vitamin pill regularly is different from 35%?

The p-value is greater than the significance level α = 0.05. So, we cannot reject the null hypothesis.

Therefore, we do not have enough evidence to conclude that the proportion taking a vitamin pill regularly is different from 35%.

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A scatter diagram is a visual method used to display a relationship between two continuous variables.

A scatter diagram, also known as a scatter plot or scatter graph, is a graphical representation of data points that helps to visualize the relationship between two continuous variables. It consists of a series of data points plotted on a Cartesian coordinate system, where one variable is represented on the x-axis and the other variable is represented on the y-axis.

Each data point on the scatter diagram represents the values of both variables for a specific observation or data point. The position of the data point on the graph is determined by the values of the two variables. For example, if one variable represents the age of individuals and the other variable represents their corresponding income, each data point on the scatter plot will represent the age and income of a specific individual.

By observing the scatter diagram, you can analyze the pattern or trend of the relationship between the two variables. The pattern may indicate a positive relationship, a negative relationship, or no apparent relationship at all.

Positive Relationship: If the data points on the scatter plot tend to form a pattern that slopes upwards from left to right, it indicates a positive relationship. This means that as the values of one variable increase, the values of the other variable also tend to increase.

Negative Relationship: Conversely, if the data points form a pattern that slopes downwards from left to right, it indicates a negative relationship. This means that as the values of one variable increase, the values of the other variable tend to decrease.

No Apparent Relationship: If the data points on the scatter plot do not form a clear pattern or exhibit a consistent trend, it suggests that there is no apparent relationship between the two variables.

Scatter diagrams are particularly useful for identifying and visualizing correlations or trends in data. They can help in determining the strength and direction of the relationship between variables, detecting outliers or anomalies, and providing insights into potential cause-and-effect relationships. They are commonly used in various fields such as statistics, data analysis, economics, social sciences, and scientific research.

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Step-by-step explanation:

4 m^2 n = 49       divide both sides of the equation by   4n

   m^2 = 49 / ( 4n)      take the square root of both sides

    m = + - 7/(2 sqrt (n))    

          rationalize the denominator on the R   ( multiply by sqrt n / sqrt n )

     m = + - 7 sqrt (n) / 2 n

Answer:

C. 12y

Step-by-step explanation:

1. 13y - (-y)+(-2y)

2. 13y + y - 2y

3. 14y - 2y

4. 12y

Answer:

19 duh

Step-by-step explanation:

Answer:

y = 7 - 2x

Step-by-step explanation:

Step 1:

2x + y = 7               Equation

Step 2:

y = 7 - 2x          Subtract 2x on both sides

Answer:

y = 7 - 2x

Hope This Helps :)

The sample space, in terms of the condition (functional or defective) of each nozzle after a year, can be represented using the symbols "f" and "d" to denote a functional and defective nozzle, respectively.

The possible outcomes in the sample space can be described as a combination of these symbols. For example, if we have three nozzles, the sample space could include outcomes such as "fff" (all three nozzles are functional), "dfd" (the first and third nozzles are functional, while the second one is defective), "ffd" (the first two nozzles are functional, while the third one is defective), and so on.

Each outcome in the sample space corresponds to a particular arrangement or configuration of functional and defective nozzles after a year. The sample space encompasses all the possible combinations and provides a comprehensive representation of the different outcomes that can occur.

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Answer: googl3

Step-by-step explanation: googl3 was made for a reason

I would start by setting up a chart like I did below.

Label one column age now and the other age in 5 years.

Since we don't know the son's age we use x.

We do know that the man's age is 4 times the son's age.

So the man's age will be 4x.

In the age in 5 year column, we add 5 to their current ages.

Now set up our equation.

Since it says "in five years" we use information in second column.

In 5 years time, he, "4x + 5", will be, equals,

3 times as old as his son, "3(x + 5)".

So we have 4x + 5 = 3(x + 5).

Solving from here, we find that x = 10.

So the son is 10 and the man is 4 times his age or 40.

Answer:

(2, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define Systems

2x + y = 5

3x - 2y = 4

Step 2: Rewrite Systems

Manipulate 1st equation

Step 3: Solve for x

Substitution

Step 4: Solve for y

Answer:

Step-by-step explanation:

To find the average cost function, we first need to understand that the average cost represents the cost per unit produced. The cost function is given as C(x) = 144 + 7.5x, where 144 represents the fixed cost and 7.5x represents the variable cost.

To calculate the average cost, we divide the total cost by the quantity produced. So, we have C(x) = C(x) / x. Substituting the cost function into this equation, we get C(x) = (144 + 7.5x) / x.

Simplifying further, we obtain C(x) = 144/x + 7.5. This equation represents the average cost per unit produced. The term 144/x represents the fixed cost component, which decreases as the quantity produced increases. The term 7.5 represents the variable cost component, which remains constant per unit produced. Therefore, the average cost function is C(x) = 144/x + 7.5.

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Type I error (also called a false positive) occurs when a null hypothesis is rejected when it is actually true. The probability of committing a Type I error is denoted by the symbol alpha (α), and is typically set at a certain level (e.g., 0.05 or 0.01) depending on the significance level desired for the hypothesis test.

Type II error (also called a false negative) occurs when a null hypothesis is not rejected when it is actually false. The probability of committing a Type II error is denoted by the symbol beta (β). The power of a statistical test is equal to 1 minus the probability of a Type II error (i.e., power = 1 - β).

Therefore, the statement that is true regarding the probability of Type I and Type II errors is that they are complementary to each other. That is, as the probability of a Type I error decreases (by setting a lower significance level), the probability of a Type II error generally increases (i.e., the power of the test decreases). Conversely, as the probability of a Type II error decreases (by increasing the sample size or effect size), the probability of a Type I error generally increases. It is important to strike a balance between controlling these two types of errors, depending on the specific goals and context of the research or hypothesis test.

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Answer:

yeah me too

Step-by-step explanation: