Solve these: state whether there is no solution, one solution specify it , or infinitely many Solutions.

Given:

z = 1.40 and z = 2.13

Let's find the area under the standard normal curve.

Let's find the score using the standard normal distribution table:

NORMSDIST(1.40) = 0.9192

NORMSDIST(2.13) = 0.9834

To find the area between them, we have:

P(1.40 < Z < 2.13) = P(Z<2.13) - P(Z<1.40) = 0.9834 - 0.9192 = 0.0642

Therefore, the area under the curve between z=1.40 and z=2.13 is 0.0642

ANSWER:

0.0642

8% of 4000 express as;

Thus, 8% of 4000 is 320

Answer : 320

...

Using the property vertically opposite angles and the corresponding angles, the value of x can be determine as,

Thus, the required value of x is 6.

Answer:

Step-by-step explanation:3x4=12x2

To answer this question, first we need to understand the definition of a median of a triangle.

A median of a triangle is a line segment drawn from a vertex to the midpoint of the opposite side of the vertex.

AB is a segment drawn from the vertex A, to the point B, but B is not the midpoint of the base of this triangle(the midpoint divides the segment into two equal parts, and since one part is 7 and the other is 8, B is not the midpoint

Given:

The sides of an equilateral triangle base are 10 yds. The height of the prism is 29 yds.

To find:

The volume of the prism.

Solution:

The formula of the volume of the triangular prism is given by:

It is known that the area of the equilateral triangle is given by:

So, the area of the base of the triangular prism is:

Now, the volume of the given triangular prism is:

Since Christi earns $21 per hour, to find how much she earns by working 19 hours per week we need to multiply the hourly wage by the number of hours she works in a week:

Her weekly wage is $399

Answer: D) $399

The first step is to define the daily rates of each pump

From the information given,

First pump can empty the pool in 7 days. This means that

Daily rate of first pump = 1/7

The first pump's rate is 1/7 per day

Second pump can empty the pool in 14 days. This means that

Daily rate of second pump = 1/14

The second pump's rate is 1/14 per day

Let t be the number of days it will take both pumps, working together to empty the pool. Thus,

combined daily rate of both pumps = 1/t

The rates are additive. It means that

1/7 + 1/14 = 1/t

Simplifying the left side, we have

3/14 = 1/t

The combined pumps rate is 3/14 per day

By taking reciprocal of both sides,

t = 14/3 = 4.67

It will take the two pumps 4.67 days to empty the pool together

Okay, here we have this:

Considering that the formula for the simple interest rate is:

A = P (1 + rt)

In this case A is equal to $2500, P is the value we need to find, r is the interest rate (in decimal) 0.08, and t is the time, so it's 3 years, replacing we obtain:

2500=P(1+0.08*3)

Now, let's clear P:

2500=P(1+0.24)

2500=P(1.24)

2500/1.24=P

P=2016.13

Finally we obtain that the bank must put $ 2016.13 on a CD to get $ 2,500 in three years.

It's important to know that synthetic division gives a polynomial as a result.

Michael obtained 7 0 24 0 0. We just need to add variables to it. As you can observe, there are 5 terms, that means the polynomial is grade 4.

Therefore, the resulting polynomial is

SOLUTION:

Step 1:

In this quesdtion, we are meant to explain the topic:

Why was Math created?"

Step 2:

The details of the solution are as follows:

1. Mathematics is a body of knowledge and knowledge and practice, that is derived from the contributions of thinkers throughout the ages and across the globe.

2. It gives us a way to understand patterns, to quantify relationships, and to predict the future.

3. Math helps us understand the world — and we use the world to understand math.

4. Excellent for your brain: Creative and analytical skills are highly desired by employers.

5. It has a lot of real-world applications.

6. It helps in better problem-solving skills.

7. Mathematics is needed in almost every career and profession.

8. Mathematics helps understand the world better.

9. Mathematics is a universal language.

10. Numbers help us understand the world, and Mathematics helps us understand numbers.

The real-life applications of Mathematics are endless.

We are surrounded by numbers, equations and algorithms – especially in this age of data science, with huge data sets that can only be understood through statistical models and analysis.

Answer:

Maths was invented to understand the world and to make measurements, do calculations etc. make and measure shapes, measure angles, and to use these things in real life. The Egyptians used the Pythagoras theorem to accurately make their pyramids.

Given :

The perimeter of a triangle is, P = 14x - 4.

The sides are, a = 3x-2 and b = 5x + 3.

The perimeter of a triangle with sides a, b and c can be expressed as,

Substituting the values, we get,

Thus, the correct option d.

If the function be [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex] then the domain of the function exists

[tex]$\left[\begin{array}{ccc}\text { Solution: } & x < \frac{5}{8} & \text { or } \quad x > \frac{5}{8} \\ \text { Interval Notation: } & \left(-\infty, \frac{5}{8}\right) \cup\left(\frac{5}{8}, \infty\right)\end{array}\right]$[/tex]

The collection of all potential inputs for a function is its domain.

Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

Let the function be [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex]

Domain of [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex] :

[tex]$\left[\begin{array}{ccc}\text { Solution: } & x < \frac{5}{8} & \text { or } \quad x > \frac{5}{8} \\ \text { Interval Notation: } & \left(-\infty, \frac{5}{8}\right) \cup\left(\frac{5}{8}, \infty\right)\end{array}\right]$[/tex]

Range of [tex]$\frac{x^3-3 x+1}{8 x-5}:\left[\begin{array}{cc}\text { Solution: } & -\infty < f(x) < \infty \\ \text { Interval Notation: } & (-\infty, \infty)\end{array}\right]$[/tex]

Axis interception points of [tex]$\frac{x^3-3 x+1}{8 x-5}[/tex]

X Intercepts: [tex]$(0.34729 \ldots, 0),(1.53208 \ldots, 0)$[/tex], [tex]$(-1.87938 \ldots, 0)$[/tex],

Y Intercepts: [tex]$\left(0,-\frac{1}{5}\right)$[/tex]

Asymptotes of [tex]$\frac{x^3-3 x+1}{8 x-5}: \quad$[/tex]

Vertical: [tex]$x=\frac{5}{8}$[/tex]

Extreme Points of [tex]$\frac{x^3-3 x+1}{8 x-5}$[/tex]

Minimum [tex]$(-0.54351 \ldots,-0.26422 \ldots)$[/tex]

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The polynomial equation with root of -1 and 2i is,

So simplest polynomial is,

You use this for the coins

Area of a circle:

r is the radius and it can be obtaided more easily if you measure the diameter of the circle and then divide it into 2.

Circunference or perimeter of a circle:

--------------------------------------------

You use this for the bills:

Aera of a rectangle:

Perimeter of a rectangle:

------------------------

The face a pyramid has the shape of a trianlge:

Area of a triangle:

Perimeter of a triangle:

Answer:

y=3^x

Explanation:

The expected payments (in cents) beginning from July 1 are given below:

Observing the payments for each subsequent day, we see that the payment for the previous day was multiplied by 3.

We can rewrite the payment as a power of 3 as follows:

Therefore, the equation will help you determine how much money you will make in July will be:

The first option is correct.

Answer: The derivative of tan(t) with respect to t is sec2(t) sec 2 ( t ) .

Step-by-step explanation:

hope this helps

The probability that the first spin lands on blue and the second spin lands on gray is 15 / 56.

Probability is the likelihood that an event will happen or take place.

The spinner has eight = sections, five of which are gray and red with your blue.

Probability that the first spin lands on blue = 8

(8 - 5)/8 = 3/8

The probability of landing of gray is 5/7 for the second time.

Therefore, the probability will be:

= 3/8 × 5/7

= 15 / 56

This illustrates the concept of probability.

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Question #5

Given:

The number of people who own computers has increased 23.2% annually since 1990

In 1990: the number of people who own computers = half a million

We will predict the number of people in 2015

We will use the following formula:

Where: (r) is the ratio of increasing = 23.2% = 0.232

And (t) the number of years after 1990

And P₀ is the initial value of the number of people

P(t) will be the number of people after (t) years

To predict the number of people in 2015

t = 2015 - 1990 = 25 years

so,

So, the answer will be:

The estimated number of people = 11.43 million

Probability that a randomly chosen applicant has a graduate degree given that they have a five years of experience = 106/441

Total number of applicants, n(Total) = 441

Number of candidates that have over five years of experience, n(5 yrs) = 235

Probability that a randomly chosen applicant has over 5 years experience

Number of applicants that have over five years of experience and have a graduate degree, n(5 n g) = 106

Probability that a randomly selected applicant has over five years of experience and have a graduate degree

Probability that a randomly chosen applicant has a graduate degree given that they have a five years of experience

Detailed Answer :-

Based on the Degree :

• A polynomial having degree 0 is called a constant polynomial.

• A polynomial having degree 1 is called a linear polynomial.

• A polynomial having degree 2 is called a quadratic polynomial.

• A polynomial having degree 3 is called a cubic polynomial.

• A polynomial having degree 4 is called a bi-quadratic polynomial.

Based on the Number of Terms :

• One term - Monomial

• Two terms - Binomial

• Three terms - Trinomial

• Four terms - Quadrinomial

All of these are generally called POLYNOMIALS.

This is the figure, roughly. We want h.

Using smaller triangle, we can write:

Also,

Now, taking the larger triangle:

The angle is 53 (30 + 23).

Let the larger side (right side) be m, which is basically:

m = h + y

Let's find m:

Now, we want height, h, which is:

m = h + y

262.62 = h + 84

h = 262.62 - 84

h = 178.62

Rounded to nearest feet

h = 179 feet

From the data provided, we can conclude:

The perimeter of the rectangle is 60m, so:

Where:

w = width

l = length

The width of the garden is 2/3 its length, therefore:

Replace (2) into (1)

Solve for l:

Replace l into (2):

We are presented with a group of graphs in which the x-axis represents time and the y-axis represents speed.

We are told that Joy started by accelerating when she took off, which means the graph should start with a line with positive slope.

She then maintained her speed, which means the slope of the line is 0, orin other words, the line is parallel to the time axis.

Finally, we are told that she saw a sign saying the speed limit had been increased, so she probably accelerated again, meaning the line should have a positive slope again.

Thus, the graph representing the situation is the third option.

1) Since Saige's spaceship makes 588 km in 60 seconds we can find its velocity:

2) After simplifying we can state:

441/45 = has the same speed as Saige's spaceship

215/25 = does not have the same speed as Saige's space

649/110 =does not have the same speed as Saige's space

The equation can be represented by

y= 25 - 2.5x

by comaprison with y = mx + c

c = 25 ( note tha c means y-intercept)

This 25 represents the initial value of the gift card

The correct answer is option d

Answer:

A

Step-by-step explanation:

h + 0.02h = (1+0.02)h = 1.02h

1.02h * 100% = 102%

102 - 100 = 2%

Answer:

[tex]x=3160.778016...[/tex]

Step-by-step explanation:

Given logarithmic equation:

[tex]\log(x)+\log(x+3)=7[/tex]

[tex]\textsf{Apply the product log law}: \quad \log_axy=\log_ax + \log_ay[/tex]

[tex]\implies \log(x(x+3))=7[/tex]

[tex]\implies \log(x^2+3x)=7[/tex]

[tex]\textsf{Apply the log law}: \quad \log_ab=c \iff a^c=b[/tex]

[tex]\implies x^2+3x=10^7[/tex]

[tex]\implies x^2+3x-10000000=0[/tex]

Solve the quadratic equation by using the quadratic formula.

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore:

[tex]a=1, \quad b=3,\quad c=-10000000[/tex]

Substitute the values of a, b and c into the quadratic formula:

[tex]\implies x=\dfrac{-3 \pm \sqrt{3^2-4(1)(-10000000)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{9+40000000}}{2}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{40000009}}{2}[/tex]

[tex]\implies x=3160.778016..., \quad x=-3163.778016...[/tex]

As logs of negative numbers cannot be taken, the only valid solution is:

[tex]\boxed{x=3160.778016...}[/tex]

A strict inequality is one which involves the use of

A non-strict inequality is one which involves the use of

A strict inequality is used in a case when the two values being compared or related to one another cannot be equal to one another. That is, they are different.

A non-strict inequality is used in case when there is a possibility that the two values being compared can be equal to one another.

The lateral area of a cone is the area of the lateral surface, except the base.

The surface area of a cone is the area of all its surface, which is the lateral side PLUS the base.

The lateral area is given by the formula >>>

The surface area is given by the formula >>>

Given

r = 10 cm

h = 24 cm

Let's find l,

Let's find the lateral area and the surface area >>>

Lateral Area =

Surface Area =