Please help I'm stuck ​

Answer:

16/33

Step-by-step explanation:

Tổng của cả 4 tấm thẻ là một số lẻ khi:

Có 1 thẻ là lẻ, 3 thẻ còn lại là chẵn, có: 6C1.5C3=60 cách

Có 3 thẻ là lẻ, 1 thẻ là chẵn, có: 5C1.6C3=100 cách

Suy ra có 160/11C4=16/33 cách

Answer:

Sure, here are the answers to your questions:

**A) The value of $f(-5)$ is $-2$.**

To find the value of $f(-5)$, we can simply substitute $x=-5$ into the equation $f(x)=-2x^2-8x+14$. This gives us:

$$f(-5)=-2(-5)^2-8(-5)+14=-2(25)+40+14=-50+54=4$$

**B) The vertex of the parabola is $(2,6)$.**

To find the vertex of the parabola, we can complete the square. This involves adding and subtracting $\left(\dfrac{{b}}{2}\right)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b=-8$, so we have:

$$\begin{aligned}f(x)&=-2x^2-8x+14\\\\ f(x)+20&=-2x^2-8x+14+20\\\\ f(x)+20&=-2(x^2+4x)\\\\ f(x)+20&=-2(x^2+4x+4)\\\\ f(x)+20&=-2(x+2)^2\end{aligned}$$

Now, if we subtract 20 from both sides, we get the equation of the parabola in vertex form:

$$f(x)=-2(x+2)^2-20$$

The vertex of a parabola in vertex form is always the point $(h,k)$, where $h$ is the coefficient of the $x$ term and $k$ is the constant term. In this case, $h=-2$ and $k=-20$, so the vertex of the parabola is $(-2,-20)$. We can also see this by graphing the parabola.

[Image of a parabola with vertex at (-2, -20)]

**C) The $y$-intercept is the point $(0,14)$.**

The $y$-intercept of a parabola is the point where the parabola crosses the $y$-axis. This happens when $x=0$, so we can simply substitute $x=0$ into the equation $f(x)=-2x^2-8x+14$ to find the $y$-intercept:

$$f(0)=-2(0)^2-8(0)+14=14$$

Therefore, the $y$-intercept is the point $(0,14)$.

**D) The two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.**

To find the values of $x$ that make $f(x)=0$, we can set the equation $f(x)=-2x^2-8x+14$ equal to zero and solve for $x$. This gives us:

$$-2x^2-8x+14=0$$

We can factor the left-hand side of the equation as follows:

$$-2(x-2)(x-3)=0$$

This means that either $x-2=0$ or $x-3=0$. Solving for $x$ in each case gives us the following values:

$$x=2\text{ or }x=3$$

However, we need to round our answers to two decimal places. To do this, we can use the calculator. Rounding $x=2$ and $x=3$ to two decimal places gives us the following values:

$$x=2.5\text{ and }x=-3.5$$

Therefore, the two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.

Answer:

56 inches (rounded)

Step-by-step explanation:

to solve this problem use the pythagreon theorem (a^2 + b^2 = c^2)

a and b represent the measurements of the side lengths of the TV in this case

plug in 27 for a and 49 for b

27^2 + 49^2 = c^2

2401 + 729 = c^2

c = 55.946 or 56

56 inches (rounded) is the length of the diagonal of the television screen.

56 inches (rounded) is the length of the diagonal of the television screen.

to solve this problem use the pythagreon theorem (a^2 + b^2 = c^2)

a and b represent the measurements of the side lengths of the TV in this case

plug in 27 for a and 49 for b

27^2 + 49^2 = c^2

2401 + 729 = c^2

c = 55.946 or 56

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a) The initial deposit in the account is given as follows: 1,287.39 euros.

b) The interest rate of the account is given as follows: 3%.

The equation that gives the balance of an account after t years, considering simple interest, is modeled as follows:

A(t) = P(1 + rt).

In which the parameters of the equation are listed and explained as follows:

Considering the balances after 5 and 6 years, the interest rate is obtained as follows:

r = 1524.60/1480.50 - 1

r = 0.03.

Considering the balance after 5 years, the initial deposit is obtained as follows:

P(1 + 0.03 x 5) = 1480.5

P = 1480.5/1.15

P = 1,287.39 euros.

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The probability that both events A and B will occur is approximately 0.4167 or 41.67%.

We must calculate the product of the probabilities of events A and B to find the likelihood that both will occur.

Event A: The coin lands on tails.

Since a coin has two possible outcomes (heads or tails), the probability of landing on tails is 1/2 or 0.5.

Event B: A 6 is not on the die.

The six faces of a conventional die are numbered from 1 to 6. On a fair dice, the likelihood of rolling a 6 is 1/6.

The likelihood of not rolling a 6 is therefore 1 - 1/6 = 5/6 or 0.8333.

We multiply the individual probabilities in order to determine the likelihood that both events will occur:

Probability of A and B = Probability of A * Probability of B

= 0.5 x 0.8333

≈ 0.4167 or 41.67%

Therefore, the probability that both events A and B will occur is approximately 0.4167 or 41.67%.

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Answer:

-1.5

Step-by-step explanation:

To work out the gradient of the line, we use this equation:

\( \frac{y2 - y1}{x2 - x1} \)

Substituting in, we get:

\( \frac{5 - ( - 4)}{ - 2 - 4} \)

Which simplifies to:

\( \frac{9}{ - 6} = \frac{3}{ - 2} = - \frac{3}{2} = - 1.5\)

Answer:

Do we do it on the graph

Step-by-step explanation:

Answer:

draw a line starting at 1 on the x axis and then have it go up to 4 on the y axis , then make the line go right until it hits the line and makes a right angle. The rise would be 4, and the run would 2 so the slope is 4/2 but since they want it simplified it's 2/1

Answer:

(1, -4)

Step-by-step explanation:

(-5,-4) -> (x,y) so x = -5 and y = -4. Apply the rule (x+6,y) to that point by substituting in your x and y values.

(-5+6,-4) = (1, -4)

Answer:

A, C, E

Step-by-step explanation:

Answer: Exact Form:

109^104

Decimal Form:

7.8046923 x 10^211

Step-by-step explanation:

Answer:

11336

Step-by-step explanation:

109*104= 11336

hdhdhdhdhdhdjudjdhdhsh

x = 85

sum of all the angles must be 540,

105 + 120 + 3x + 35 + 25 = 540

3x = 255

x is 85

The correct answer in terms of percentage is 10.4%.

According to the question, the given expression can be written in terms of percentage which is as shown below:

Let us assume, percentage be 'a'.

Required expression: (a%) 1600 = 2300

⇒(a%) = 2300/1600 = 23/16 = 10.4

⇒ a = 10.4%

Hence, the correct answer in terms of percentage is 10.4%.

What is percentage?

The word percentage can be calculated by dividing the given value with the total value. And later multiply it with hundred. And also, it is one-by-hundred term.

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The equivalent expression for the given expression is -2i(-8+4i).

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 8 +16i.

The given expression can be written as 8(1+2i)

-2i(-8+4i)

= -2i×(-8)-(-2i)×4i

= 16i-8i²

= 16i-8(-1)

= 8+16i

Therefore, the equivalent expression is -2i(-8+4i).

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Answer:636

Step-by-step explanation: I just kno

Answer:

The equation that models the situation is \(y = 8 - 0.75t\)

Step-by-step explanation:

Equation of a line:

The equation of a line, in slope-intercept formula, has the following format:

\(y = mx + b\)

In which m is the slope(how much y changes when x changes by 1 unit) and b is the intercept, which is the value of t when x = 0.

A candle is 8 inches tall and burns at 3/4 inch each hour.

Using t as number of hours and y as the height.

Initial height of 8 inches, that is, when \(t = 0, y = 8\), so \(b = 8\)

Burns at 3/4 inch each hour.

That is, the height decreases by a rate of 3/4 inch each hour, so \(m = -\frac{3}{4} = -0.75\)

So

\(y = 8 - 0.75t\)

Answer:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Step-by-step explanation:

To solve this problem, we'll consider the velocities of the cruise ship and the Gulf Stream as vectors and calculate their components and resultant vector. Then we'll find the magnitude (resultant velocity) and direction (resultant direction) of the resultant vector.

Given:

Cruise ship velocity (south): 22 mph

Gulf Stream velocity (east): 4 mph

A) Vector component for the cruise ship:

The cruise ship is traveling south, so its velocity vector is (0, -22).

B) Vector component for the Gulf Stream:

The Gulf Stream is flowing east, so its velocity vector is (4, 0).

C) Resultant vector:

To find the resultant vector, we'll add the two velocity vectors together:

Resultant vector = Cruise ship velocity + Gulf Stream velocity

Resultant vector = (0, -22) + (4, 0)

Resultant vector = (0 + 4, -22 + 0)

Resultant vector = (4, -22)

D) Resultant velocity:

The magnitude of the resultant vector gives us the resultant velocity. We can use the Pythagorean theorem to calculate it:

Resultant velocity = sqrt((x-component)^2 + (y-component)^2)

Resultant velocity = sqrt((4)^2 + (-22)^2)

Resultant velocity = sqrt(16 + 484)

Resultant velocity = sqrt(500)

Resultant velocity ≈ 22.4 mph (rounded to the nearest tenth)

E) Resultant direction:

The direction of the resultant vector can be found using trigonometry. We'll use the inverse tangent function (arctan) to find the angle between the resultant vector and the positive x-axis.

Resultant direction = arctan(y-component / x-component)

Resultant direction = arctan(-22 / 4)

Resultant direction ≈ -1.405 radians or -80.5 degrees (rounded to the nearest tenth)

Therefore, the answers are:

A) Vector component for the cruise ship: (0, -22)

B) Vector component for the Gulf Stream: (4, 0)

C) Resultant vector: (4, -22)

D) Resultant velocity: Approximately 22.4 mph (rounded to the nearest tenth)

E) Resultant direction: Approximately -80.5 degrees (rounded to the nearest tenth)

Answer: 171 attendees

Step-by-step explanation:

I answered another similar question by you earlier, so I really hope you read through this explanation, as I will go far in depth.  It's important you learn to do this so as not to simply skate through homework, then struggle with assessment.

For this problem, you have to find something called a unit price.

A unit price is the price in dollars per thing.

In this case, the price in dollars for the whole group is $132 for many things, 66 attendees.

Because 66 attendees costs $132, to find out how much money a single attendee costs, simply divide $132 by 66 to get 2$ for 1 attendee.

With this information, it is very straightforward to determine the number of attendees for $342.  Simply divide $342 by $2 to get 171 attendees.

I really hope it helps :) and please, let me know if you want me to explain in more depth, the unit you are currently in is a fundamental part of early math, and it is important you understand it.

Using the properties of parallel line and similar triangle we calculate the length of the side DG to be 19.4 units .

In triangle ACF by using the properties of Pythagoras Theorem we can say that

AC² = FA² + CF²

Given:

AC = 10 , FA = 6

∴10² = 6² + CF²

or, CF = 8 units.

Now in triangles ΔACF and triangle ΔADG

CF is parallel to DG , therefore the two triangles are similar.

therefore we can say that using the properties of similar triangle we will use the ratio of the sides to find the given side.

AC/AD=CF/DG

or, 10/24 = 8 / DG

or, DG = 192 /10

or, DG = 19.2 units

Triangles that share the same form but differ in size are said to be similar. All equilateral triangles and squares with equal sides serve as examples of related items.

In other words, two similar triangles have similar sides that are proportionately equal and similar angles that are congruent.

Hence the length of the side is 19.2 units.

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Answer:

bottom right

Step-by-step explanation:

all of the others are the wrong shape or do not fully make the rectangle it is the bottom right one.

the correct option is D:

" The inverse relation must pass the vertical line test."

Remember that a relation is only a function if each value in the domain is only mapped into a single value in the range.

All functions need to pass what is called the "vertical line test" this means that if you draw a vertical line on the graph of the function, the vertical line can intersect the graph at most one time. If the vertical line intercepts the graph two or more times, then it is not a function.

From this we conclude that the correct option is D:

" The inverse relation must pass the vertical line test."

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The correct expanded form using Laws of exponents is:

Two-thirds times two-thirds times two-thirds times two-thirds

Some of the laws of exponents are:

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

Now, we want to solve the expression given as: (²/₃)⁴

When we expend this, we arrive at:

²/₃ × ²/₃ × ²/₃ × ²/₃

This among the options is Option A which is:

Two-thirds times two-thirds times two-thirds times two-thirds

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Answer:

  Option 1

Step-by-step explanation:

You want to know which of 4 tables shows a non-linear function.

A function represented by a data table will be linear if the ratios of changes in y to changes in x are the same for all intervals.

Changes in y are ...

  -10 -(-4) = -6, -8, -10

Changes in x are ...

  10 -8 = 2, 2, 2

The ratios of these changes are ...

  -6/2 = -3, -8/2 = -4, =10/2 = -5

These are not constant, so this table is a nonlinear function.

Changes in y are ...

  8 -10 = -2, -8, -6

Changes in x are ...

  -2 -(-3) = 1, 4, 3

The ratios of these changes are ...

  -2/1 = -2, -8/4 = -2, -6/3 = -2

These are constant, so this table is a linear function.

The nonlinear function is Option 1.

__

Additional comment

The ∆y/∆x ratios for Option 3 are all -10/3. For Option 4, they are all 2.

Answer:

y=1

Step-by-step explanation:

When x= -4, y=1, i don't know how else to explain it. Find the y value of the graph at that point.

Answer:

y=1

Step-by-step explanation:

if we look at the graph at x-axis where x= -4 and go to meet the line graph , now look at the y -axis and see y= 1

The population of Kentucky is nearly 5.9 times that of North Dakota.

To determine how many times larger Kentucky's population is than North Dakota's population, divide Kentucky's population by North Dakota's population:

4.47 x 10^6 / 7.62 x 10^5

We can simplify the fraction by dividing both the numerator and denominator by 7.62 x 10: 4.47 x 106 / 7.62 x 105 = 5.87

5.9, rounded to the closest tenth.

As a result, the population of Kentucky is nearly 5.9 times that of North Dakota.

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Answer:

40 miles

Step-by-step explanation:

She wants to run x miles.

She already ran 24 miles, and that is 60% of x.

60% of x = 24

0.6x = 24

x = 24/0.6

x = 40

Answer: 40 miles

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

104 ft²

Step-by-step explanation:

Multiply base × height.

Using the formula of volume of a sphere and hemisphere, the volume of the figures are given as;

1. 2144.57 m³

2. 696.6 m³

3. 20569.1m³

4. 2637ft³

5. 56.5km³

6. 6381.79 in³

The volume of a sphere is given as 4/3πr³

Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.

1. The volume of the sphere is;

v = 4/3 * 3.14 * 8³ = 2144.57m³

2. The volume of the sphere is;

v = 4/3 * 3.14 * (11/2)³ = 696.6m³

3. The volume of the sphere is;

v = 4/3 * 3.14 * 17³ = 20569.1m³

4. The volume of the hemisphere is;

v = 2/3 * 3.14 * 10.8³ = 2637ft³

5. The volume of the hemisphere is;

v = 2/3 * 3.14 * 3³ = 56.5km³

6. The volume of the hemisphere is;

v = 2/3 * 3.14 * (29/2)³ = 6381.79in³

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Answer:

When x = 1, (f◦g)(x) is -2.

Step-by-step explanation:

Composite function:

The composite function of f and g is given by:

\((f \circ g)(x) = f(g(x))\)

In this question:

\(f(x) = x - 3, g(x) = x^2\)

Composite function:

The composite function is:

\(f(g(x)) = f(x^2) = x^2 - 3\)

At x = 1

\((f \circ g)(1) = 1^2 - 3 = 1 - 3 = -2\)

So

When x = 1, (f◦g)(x) is -2.