In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?
r > 4 and r ≤ 4.1
r > 4 or r ≤ 4.1
r < 4 and r ≥ 4.1
r < 4 or r ≥ 4.1

Answer:

a) 25830

b)9975

Step-by-step explanation:

a) 287

x 90

25830

b) 105

x 95

9975

The measure of the ∠1 is 35 degrees.

it is important to know that the measure of an angle with its vertex outside the circle is half the difference of the intercepted arcs.

Also, the angle subtended by the arc at the center of the circle is the angle of the arc

From the diagram, we have

m ∠ of external angle = half of the difference of arc angles

The arc angles are

m ∠ of external angle = ∠ 1

Let's substitute the angles

∠1 = [tex]\frac{106 - 36}{2}[/tex]

∠ 1 = [tex]\frac{70}{2}[/tex]

∠ 1 = 35°

We can see that the external angle 1 measures 35 degrees.

Note that the complete image is added.

Thus, the measure of the ∠1 is 35 degrees.

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The lowest score you can earn and still be eligible for employment is 85.6925.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean  and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

Top 5%.

At least the 100-5 = 95th percentile.

The 95th percentile is X when Z has a pvalue of 0.95. So X when Z = 1.645.

x-75 = 1.645*6.5

x = 85.692

Thus the lowest score you can earn and still be eligible for employment is 85.6925.

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The ratio for Rowan = 4:1.

The ratio for Marcia = 10:1.

The ratio for Jillian = 5:1.

The ratio for Lulua = 6:1.

The smallest ratio among these for purple to white flowers is for Rowan, that is, 4:1.

Ratios are fractions in the simplest form representing the relationship between two quantities.

The ratio of purple to white flowers for each friend can be shown as:-

Rowan:

The number of purple flowers = 8

The number of white flowers = 2

Thus, the fraction of purple to white flowers = 8/2 = 4/1.

Thus, the ratio for Rowan = 4:1.

Marcia:

The number of purple flowers = 10

The number of white flowers = 1

Thus, the fraction of purple to white flowers = 10/1.

Thus, the ratio for Marcia = 10:1.

Jillian:

The number of purple flowers = 10

The number of white flowers = 2

Thus, the fraction of purple to white flowers = 10/2 = 5/1.

Thus, the ratio for Jillian = 5:1.

Lulua:

The number of purple flowers = 18

The number of white flowers = 3

Thus, the fraction of purple to white flowers = 18/3 = 6/1.

Thus, the ratio for Lulua = 6:1.

The smallest ratio among these for purple to white flowers is for Rowan, that is, 4:1.

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Answer:Its rowan

Step-by-step explanation:Mark me brainliest need award

The order of the numbers which satisfies commutative property exists 1/7 + (-1)+ 2/7.

The commutative property exists a math rule that states that the order in which we multiply numbers does not change the product. The commutative property uses for addition and multiplication. The property states that phrases can “commute,” or transfer locations, and the outcome will not be affected. This exists described as a + b = b + a for addition, and a × b = b × a for multiplication.

Arranging the order of the numbers the fractions

[tex]$& \frac{1}{7}+(-1)+\frac{2}{7} \\[/tex]

[tex]$=& \frac{1}{7}+\frac{2}{7}+(-1) \\[/tex]

Simplifying the equation, we get

[tex]$= \frac{1}{7}+(-1) \\[/tex]

[tex]$&=\frac{4}{7}[/tex]

Therefore, the correct answer is option A. 1/7 + (-1)+ 2/7

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The value of a + b + c based on the product formula is 8.

From the information given, the product of the proper divisor is illustrated.

Based on the information, the addition of the symbols will be:

= a + b + c

= 3 + 3 + 2

= 8

In conclusion, the correct option is 8.

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Check each number's prime factorization, then add any factors necessary to make each one a cube.

(a) 3

[tex]3087 = 3^2 \times 7^3 \implies \boxed{3}\times3087 = (3\times7)^3 \implies 9261=21^3[/tex]

(b) 25

[tex]2560 = 2^9\times5^1 \implies \boxed{5^2}\times2560 = \left(2^3\times5\right)^3 \implies 64000 = 40^3[/tex]

The missing side of a right triangle x is 24 units.

A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.

The side x can be found using similar triangle ratios,

Hence,

x / 400 = 144 / x

cross multiply

x × x = 400 × 144

x² = 57600

square root both sides

√x² = √57600

x = 240

Therefore, the value of x in the right triangle is 240 units.

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The correct option is (d) Mutually exclusive events.

Let a and b be the events of the fda approving and rejecting a new drug to treat hypertension, respectively. The events a and b are mutually exclusive events.

Two events are mutually exclusive or disjoint in logic and probability theory if they cannot both occur at the same time. The results of a single coin toss, which can result in either heads or tails but not both, provide a clear illustration.

A statistical term used to describe events that cannot occur concurrently is "mutually exclusive." It is frequently used to refer to circumstances in which the occurrence of one event takes precedence over the other. For instance, it is impossible for war and peace to exist together. They are therefore opposed to one another.

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The linear inequality of the graph is: -x + 2y + 1 > 0

First, we calculate the slope of the dashed line using:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Two points on the graph are:

(1, 0) and (3, 1)

The slope (m) is:

[tex]m = \frac{1 - 0}{3 - 1}[/tex]

This gives

m = 0.5

The equation of the line is calculated as:

[tex]y = m(x -x_1) + y_1[/tex]

So, we have;

[tex]y = 0.5(x -1) + 0[/tex]

This gives

[tex]y = 0.5x -0.5[/tex]

Multiply through by 2

[tex]2y = x - 1[/tex]

Now, we convert the equation to an inequality.

The line on the graph is a dashed line. This means that the inequality is either > or <.

Also, the upper region of the graph that is shaded means that the inequality  is >.

So, the equation becomes

2y > x - 1

Rewrite as:

-x + 2y + 1 > 0

So, the linear inequality is: -x + 2y + 1 > 0

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Complete question

Find a linear inequality with the following solution set. Each grid line represents one unit. (Give your answer in the form ax+by+c>0 or ax+by+c [tex]\geq[/tex] 0 where a, b, and c are integers with no common factor greater than 1.)

The x-values are the heartbeat(s) and the y-values are the time(s)

The variables are given as:

Time(s) and Heartbeat(s)

As a general rule, the action that is being done is the independent variable.

The action here is the heartbeat.

So, the x-values are the heartbeat(s) and the y-values are the time(s)

A possible value of this is;

x = 100, y = 60 seconds

So, the ordered pair is (100,60)

When represented as ratio, we have;

Ratio = 60/100

Simplify

Ratio = 0.6 heartbeat per second

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Answer:

The total surface area of the the cylinder is 640.56cm², surface are is always give in cm² not in cm³ b/c cm³ indicates the volume of the cylinder not the surface area.

Step-by-step explanation:

Hello!

. SA=2πr(r+h) ,or 2πr²+h(2πr)

Answer:

204π cm^2

which is 640.88 cm^2 to the nearest hundredth.

Step-by-step explanation:

Surface area = 2 * area of the base + area of the curved side.

= 2*π *r^2  + 2*π*r*h

= 2π(6)^2 + 2π(6)(11)

= 72π + 132π

= 204π cm^2.

The y-intercept of the linear function is y = 0.

A linear function is modeled by:

y = mx + b

In which:

The y-intercept is given by (0,a) = (0,-a). From this, we have that for it to be a function, a = -a, and the only value that respects this condition is a = 0, hence the y-intercept of the linear function is y = 0.

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As x increases, y value decreases.

The rate of change for y as a function of x is decreasing, therefore the function is a decreasing function.

For all values of x, the function value y, decreases to 0.

The y intercept of the graph is the function value y=8

When x=1, the function value y=5.

From the given graph, it is clear that the curve is decreasing for all values of x. Hence, the rate of change of the give curve is decreasing.

Therefore, the giving function is called as decreasing function.

Since, the function is decreasing for all values of x, the value of y decreases to 0.

Form the graph, it is clear that the y-intercepts is at y=8.

Also, the value of y at x=1 is 5 from the graph.

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Answer:

In math, calculus deals with the finding and properties of derivatives and integrals of functions, by methods originally based on the summation of infinitesimal differences. The two basic types of calculus are differential calculus and integral calculus.

Step-by-step explanation:

hope it helps

sorry if I'm wrong

Answer:

A, B, F

- The radius of the circle is 3 units

- The center of the circle lies on the x-axis

- The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9

Step-by-step explanation:

The first option is correct because the standard equation of the circle is:

[tex](x - 1)^{2} + {y}^{2} = 9[/tex]

making the radius equal to 3.

The center is at (-1,0), therefore it lies on the x-axis.

And lastly, the last option is correct because both options have the radius of 3.

Answer:

The answer is 75 and here's why.

Let's figure out the amount of remaining votes to prove this.

250 total votes   -    150 votes for candidate a = 100 votes.

               minus ↑ sign

Candidate B received 25% of the votes, so let's find 25% of 100

100 * 0.25 = 25 votes

Candidate B only got 25 votes (that's kinda sad, poor guy)

100 - 25 votes = the # of votes candidate C got

Candidate C got 75 votes!

Answer:

[tex]\huge\boxed{\sf Option \ B}[/tex]

Step-by-step explanation:

[tex]\displaystyle x^2+\frac{bx}{a} =\frac{-c}{a}[/tex] --------------------(1)

Take the expression

[tex]\displaystyle x^2 + \frac{bx}{a}[/tex]

We can also write it as:

[tex]\displaystyle (x)^2 + 2(x)(\frac{b}{2a} )[/tex]

According to the formula [tex]a^2+2ab+b^2[/tex], the b of this expression is [tex]\displaystyle \frac{b}{2a}[/tex]. So,

b² will be:

[tex]\displaystyle =(\frac{b}{2a} )^2\\\\=\frac{b^2}{4a^2}[/tex]

So, we will add [tex]\displaystyle \frac{b^2}{4a^2}[/tex] to both sides in Eq. (1)

For STEP 4, the equation will become:

[tex]\displaystyle x^2+\frac{bx}{a} + \frac{b^2}{4a^2} = \frac{-c}{a} + \frac{b^2}{4a^2}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

Below in bold.

Step-by-step explanation:

The next step is to divide b/a by 2 then square it and add to both sides.

This creates a perfect square quadratic on left side.

So the answer is :

x squared plus b over a times x plus quantity b over 2 times a all squared equals negative c over a plus quantity b over 2 times a all squared

The height of squared pyramid is [tex]\frac{1}{3}h[/tex] unit.

A cube is a solid three-dimensional object with six square faces or sides, three of which meet at each vertex. One of the five Platonic solids, the cube is the only regular hexahedron. It contains 8 vertices, 6 faces, and 12 edges.

Volume of cube [tex]= (side)^3 \ unit^3[/tex]

Given the height of cube is [tex]h[/tex] unit.

Volume of cube is [tex]h^3 \ unit^3[/tex]

Let the height of squared pyramid is [tex]x[/tex] unit

Volume of squared pyramid is [tex]\frac{1}{3} h^{2} \times x \ unit^3[/tex]

According to the question, we have

Volume of cube = [tex]6 \times[/tex] volume of squared pyramid

[tex]\Rightarrow h^3=6 \times \frac{1}{3}h^2 \times x\\\Rightarrow h^3=2 \ h^2 \times x\\\Rightarrow h=2x\\\Rightarrow x= \frac{1}{2}h[/tex]

Therefore, the height of squared pyramid is [tex]\frac{1}{3}h[/tex] unit.

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Combining the equations, the solution to the system of equations is: x = 3, y = 10.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

Combining(adding) them, we have that:

5x - 3y = -15.

From the second equation:

y = 3x + 1.

Replacing in the combined equation:

5x - 3(3x + 1) = -15.

-4x = -12

x = 3.

y = 3x + 1 = 3 x 3 + 1 = 10.

The solution is:

x = 3, y = 10.

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Answer:

[tex]\displaystyle \\\sum_{k=0}^4 45-2.5k=200[/tex]

Step-by-step explanation:

We start off with the term 45 and decrease by 2.5 each term, ending with four 2.5's subtracted from 45.

Therefore, our index starts at k=0 and ends at 4. The general term can be defined then as [tex]\displaystyle \\\sum_{k=0}^4 45-2.5k[/tex] and evaluating yields 200.

From the proof of modular congruence below, it has been shown that;

41 ≡ 21 (mod 3).

We want to use the definition of modular congruence to prove that;

41 is congruent to 21 (mod 3) i.e if a ≡ b (mod m) then b ≡ a (mod m).

We are trying to prove that modular congruence mod 3 is a symmetric relation on the integers.

First, if we recall the definition of modular congruence:

For integers a, b and positive integer m,  

a ≡ b (mod m) if and only if m|a–b

Suppose 41 ≡ 21 (mod 3).

Then, by definition, 3|41–21, so there is an integer k such that 41 – 21 = 3k.

Thus;

–(41 – 21) = –3k

So

21 – 41 = 3(–k)

This shows that 3|21 – 41.

Thus;

21 ≡ 41 (mod 3) and the proof is complete

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Answer:

151 19/27 in^3

Step-by-step explanation:

volume of cube is (side length)^3

(5 1/3)^3 = (16/3)^3 = 4096/27 = 151 19/27

If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.

Let the total number of games played by Perry be x.

It is given that, Salazar played 13 more tennis games than Perry.

⇒ Total games played by Salazar = x + 13

Also, Salazar and Perry played a combined of 53 games.

Hence, total number of tennis games played by Salazar and Perry = 53

⇒ Games played by Salazar + Games played by Perry = 53

⇒  x + (x + 13) = 53

2x + 13 = 53

2x = 53 - 13

2x = 40

x = 40 / 2

x = 20

Therefore, total number of games played by Salazar = x+13

= 20 + 13

= 33

Thus, Salazar played total 33 games.

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The amount of money Mario will have if he puts $1000 in a savings account earning 4% annually after 10 years is $1,480

A = p(1 + r)^t

A = p(1 + r)^t

= 1000(1 + 0.04)^10

= 1000(1.04)^10

= 1000(1.48)

A = $1,480

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#1

#b

#c

#f

#i

Answer:

a) 3₁₀

b) 6₁₀

c) 7₁₀

f) 19₁₀

i) 181₁₀

Step-by-step explanation:

Binary to Decimal Conversion (Positional Notation Method)

For a binary number with 'n' digits:

For example, to convert the binary number 111001₂ into a decimal:

[tex]\begin{array}{ c c c c c c}1 & 1 & 1 & 0 & 0 & 1\\\downarrow & \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\2^5 & 2^4 & 2^3 & 2^2 & 2^1 & 2^0\\\end{array}[/tex]

Multiply each digit by the base (2) raised to the power as indicated above and sum them:

[tex]=(1 \times 2^5)+(1 \times 2^4)+(1 \times 2^3)+(0 \times 2^2)+(0 \times 2^1)+(1 \times 2^0)[/tex]

[tex]= 32+16+8+0+0+1[/tex]

[tex]= 57[/tex]

Finally, express as a decimal number ⇒ 111001₂ = 57₁₀

Question (a)

[tex]\begin{aligned}\implies 11_2 & = (1 \times 2^1)+(1 \times 2^0)\\& = 2+1\\& = 3\end{aligned}[/tex]

Therefore, 11₂ = 3₁₀

Question (b)

[tex]\begin{aligned}\implies 110_2 & = (1 \times 2^2)+(1 \times 2^1)+(0 \times 2^0)\\& = 4+2+0\\& = 6\end{aligned}[/tex]

Therefore, 110₂ = 6₁₀

Question (c)

[tex]\begin{aligned}\implies 111_2 & = (1 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =4+2+1\\& = 7\end{aligned}[/tex]

Therefore, 111₂ = 7₁₀

Question (f)

[tex]\begin{aligned}\implies 10011_2 & =(1 \times 2^4)+(0 \times 2^3)+ (0 \times 2^2) +(1 \times 2^1)+(1 \times 2^0)\\& =16+0+0+2+1\\& = 19\end{aligned}[/tex]

Therefore, 10011₂ = 19₁₀

Question (i)

[tex]\phantom{)))}10110101_2 \\\\=(1 \times 2^7)+(0 \times 2^6)+(1 \times 2^5)+(1 \times 2^4)+(0 \times 2^3)+ (1 \times 2^2) +(0 \times 2^1)+(1 \times 2^0)\\\\=128+0+32+16+0+4+0+1\\\\= 181[/tex]

Therefore, 10110101₂ = 181₁₀