The values of the expressions when evaluated are 10000 and 1000
How to evaluate both expressions.From the question, we have the following parameters that can be used in our computation:
There are about 10 ^ 4 different species of birds on Earth. Just over 10 ^ 3 of them are threatenedThis means that
Species = 10^4 = 10000
Threatened = 10^3 = 1000
Hence, the values are 10000 and 1000
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2x-5/ x^2-6x-7< 1/x-3
The solution is x^2-5x+22<0.
What is inequality?An inequality is a relation which makes a non-equal comparison between two numbers or mathematical expressions.
here, we have,
2x-5/ x^2-6x-7< 1/x-3,
so, we get,
⇒2x-5/x^2-7x+x-7 < 1/x-3
⇒2x-5/(x-7)(x+1) < 1/x-3
⇒2x-5 * x-3 < (x-7)(x+1)
⇒2x^2-11x+15 < x^2-6x-7
⇒x^2-5x+22<0
Hence, The solution is x^2-5x+22<0.
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Find each exact value if 0
Tan (x - y) if csc x = 13/5 and cot y = 4/3
Using trigonometry formulas, the value of tan(x-y) = -16/63
What is trigonometry?In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied. Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.
Given
cot y = 4/3
1/tan y = 4/3
Cross multiply
tan y = 3/4
Also since csc x = 13/5
1/sin x = 13/5
sin x = 5/13
Since sin x = opp/hyp
opp = 5
hyp = 13
Get the adjacent
hyp² = opp²+adj²
13² = 5²+adj²
adj² = 13² - 5²
adj² = 169 - 25
adj² = 144
adj = 12
cos x = adj/hyp
cos x = 12/13
tan x = sin x/ cos x
tan x = (5/13)/(12/13)
tan x = 5/13 * 13/12
tan x = 5/12
tan(x-y) = tan x - tan y/1 + tan x * tan y
tan(x-y) = (5/12 - 3/4) / 1 + (5/12) (3/4)
tan(x-y) = (5-9/12) / 1 + 5/16
tan(x-y) = -4/12/(21/16)
tan(x-y) = -1/3 * 16/21
tan(x-y) = -16/63
the value of tan(x-y) is -16/63
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solve In (2x-3) = 1/2
2. There are 6 children that each want to eat half of a chocolate bar. If they buy a package of 4 chocolate bars, how many chocolate bars will be left over after they've eaten?
Answer:
1
Step-by-step explanation:
6 children that each want to eat half of a chocolate bar (0.5)
6 * 0.5 = 3 - chocolate bars will be eaten
They bought a package of 4 chocolate bars
4 - 3 = 1 - chocolate bar will be left
Math Journal At a county fair, a strip of 20 ride tickets costs $13. The manager thinks they should also sell a strip of 8 ride tickets. Describe how the manager can use a unit rate to decide on a fair price for the strip of 8 tickets.
Answer:
20/13=1.54
1.54*8=12.32
The manager can use the unit rate, the price of one ticket to find the price of 8 tickets by doing the steps above.
Step-by-step explanation:
Stacy was a stay-at-home mom for most of her adult life. At age 46, she started working outside the home. Each year she earns the maximum number of Social Security credits. Until what age must she work to qualify to receive Social Security benefits when she retires?
The age that she must work till she is qualified to receive Social Security benefits when she retires is: 56 years
What is the timeframe for Social Security benefits?Social Security benefits provide partial replacement income for retired beneficiaries and disabled persons, as well as their spouses, children and survivors.
To be eligible for Social Security benefits, you must be enrolled in the Social Security program and accumulate 40 credits while employed.
Benefits are based on your income history, year of birth, and age at which you began applying for Social Security.
If your spouse is unemployed or has not reached the required number of credits, you can receive benefits according to your spouse's work performance.
Benefits may likely be taxed based on the specific income and tax return status.
She will be required to earn a total of 40 credits in order to qualify to be able to receive social security benefits, due to the fact that she earns the maximum number of 4 credits per year, she therefore has to work for at least a minimum of ten years or until at least she is 56.
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Let $x=\frac{7}{8}$ and $y=-\frac{2}{9}$. If $x\cdot z = y$, then what is $z$?
The value of z is found by dividing y by x, which results in z =[tex]-\frac{16}{63}$[/tex]
To solve for z, we can use the equation [tex]$x\cdot z = y$[/tex]. We know that [tex]$x = \frac{7}{8}$[/tex] and [tex]$y = -\frac{2}{9}$[/tex],
Therefore, we can enter these values into the equation as substitutes:
[tex]$\frac{7}{8} \cdot z = -\frac{2}{9}$[/tex]
Next, In order to separate z, we must divide both sides of the equation by [tex]$\frac{7}{8}$[/tex]:
[tex]$z = \frac{-\frac{2}{9}}{\frac{7}{8}}$[/tex]
To divide by[tex]$\frac{7}{8}$[/tex], The fraction can be rotated, then multiplied by its reciprocal, which is [tex]$\frac{8}{7}$[/tex]
[tex]$z = \frac{-\frac{2}{9}}{\frac{7}{8}} \cdot \frac{8}{7}$[/tex]
The fraction on the right can be made simpler as follows:
[tex]$z = -\frac{2}{9} \cdot \frac{8}{7} = -\frac{16}{63}$[/tex]
So, The value of z is found by dividing y by x, which results in z =[tex]-\frac{16}{63}$[/tex]
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PLEASE HELP ASAP PLEASE CORRECT
Answer: C,A,D
Step-by-step explanation:
PLS I NEED HELP I WILL SELL MY SOUL AND MY BODY PLS ILL DO ANYTHING!
Answer:
53 and 3/5's of a percent
Step-by-step explanation:
A spinner is divided into three equal parts A, B, and C. The repeated experiment of spinning the spinner twice is simulated 125 times. A table of outcomes is shown.
The probability you expect the spinner to not land on B is 0.4.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, a spinner is divided into three equal parts A, B, and C.
The repeated experiment of spinning the spinner twice is simulated 125 times.
The total number of outcomes = 125
The number of favorable outcomes = 12+18+15+17+13= 75
Probability of landing on B = 75/125
= 0.6
Probability of not landing on B
= 1-0.6
= 0.4
Therefore, the probability you expect the spinner to not land on B is 0.4.
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"Your question is incomplete, probably the complete question/missing part is:"
A spinner is divided into three equal parts A, B, and C. The repeated experiment of spinning the spinner twice is simulated 125 times. A table of outcomes is shown.
Based on the table, for what probability can you expect the spinner to not land on B?
(A) 0.10
(B) 0.33
(C) 0.40
(D 0.66
You made it onto the game show Let's Make a Deall You are chosen for the opportunity to win some cash! You are
presented with a bag that contains 5 $100 bills, 9 $20 bills, 17 $5 bills, and 42 $1 bills. (write probabilities in
simplified fraction / ratio form)
Wayne says you can draw three bills randomly from the bag for your prize (you keep each bill you draw). What is
the probability of winning $300?
Unfortunately, you draw three $1 bills! Wayne feels for you and says you can put two of the bills back into the bag
(replace the bills). What is the probability of winning $201?
A train consists of 36 carriages. There were 1,400 passengers on the train. In every ten consecutive carriages, there will be 398 passengers How many passengers occupy 4 middle carriages of the train ?
Answer:
4 middle carriages have 162 passengers
Step-by-step explanation:
Since every 10 consecutive carriages have 398 passengers, then each carriage has 398/10 = 39.8 passengers.
Since there are 36 carriages in the train, then there are 36 * 39.8 = 1428 passengers in the train.
Therefore, there are 1400 - 1428 = -28 passengers missing.
This means that each carriage has 39.8 - (-28/36) = 39.8 + 0.78 = 40.58 passengers.
So, the 4 middle carriages have 4 * 40.58 = 162.32 passengers.
Rounding to the nearest whole number, we can say that 4 middle carriages have 162 passengers.
Answer:
192
Step-by-step explanation:
If a train with 36 carriages holds 1400 passengers, 398 in any 10 consecutive carriages, you want to know the number in the 4 middle carriages.
ModelThe first 30 carriages will hold 3·398 = 1194 passengers, so there must be 1400 -1194 = 206 in the remaining 6 carriages. The same would be true counting carriages from the other end.
Then the 10 +6 carriages at either end of the train must hold 398 +206 = 604 passengers. That leaves 1400 -2·604 = 192 passengers in the middle 4 carriages.
help please i need help im not smart
Step-by-step explanation:
The objective Felipe had was to solve for x. The first step to do is to try to balance each side. He subtracted 3x from 2x which got him -x+6=-8 , since 2x - 3x equals -1x and the 3x minus the 3x cancels out. I hope this helps!
A house is 32 feet wide and has a gable with rafters 22 feet long, excluding the part which projects below the eaves. Find the pitch of the roof, or the angles between the rafter and the horizontal.
The pitch of the roof is roughly 35.3 degrees, and the middle height of the roof is 19.3 feet.
What is Pythagoras theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship in Euclidean geometry between the three sides of a right triangle. It indicates that the area of the hypotenuse square is equal to the sum of the areas of the squares on the other two sides.
Here,
To find the pitch of the roof, we need to use the Pythagorean theorem to determine the height of the roof at the center. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).
In this case, the height of the roof at the center is the hypotenuse, and the two shorter sides are the width of the house (32 feet) and half of the length of the rafter (22 feet / 2 = 11 feet). So, using the Pythagorean theorem, we can set up the following equation:
h² = (32 / 2)² + 11²
h² = 16² + 11²
h² = 256 + 121
h² = 377
h = √377
h = 19.3 feet
Next, we use the tangent function to find the pitch of the roof. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the roof (19.3 feet), and the adjacent side is half of the rafter length (11 feet). So, we can set up the following equation:
tan(pitch) = 19.3 / 11
We can use the inverse tangent function (tan^-1) to find the angle, which will give us the pitch of the roof in degrees.
pitch = tan^-1(19.3 / 11)
The pitch of the roof is approximately 35.3 degrees and height of the roof at the center is 19.3 feet.
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If A (2,-5) and A' (-6, 15), write a rule to describe the translation.
We subtract 8 from the x-coordinate and add 20 to the y-coordinate of the original point.
What do you mean by translation?In mathematics, translation refers to the process of moving an object from one location to another, without rotating or scaling it. The movement is described by a vector, which is a directed line segment that specifies the direction and distance of the movement.
In two-dimensional geometry, a translation can be represented by a shift of an object along the x- and y-axes. For example, if a point is translated by a vector (a, b), its new position will be (x + a, y + b), where (x, y) is the original position of the point.
Translations can also be performed on shapes, such as lines, polygons, or curves. The effect of a translation on a shape is to create a new shape that is identical to the original shape, but located in a different position.
A translation is a transformation that moves a figure in a certain direction and by a certain distance without rotating or reflecting it. To find the rule for a translation, we need to find the vector that represents the displacement between the original point and the translated point.
Given two points A (2, -5) and A' (-6, 15), the translation vector is given by:
Translation vector = A' - A = (-6, 15) - (2, -5) = (-6 - 2, 15 - (-5)) = (-8, 20)
So, the rule for the translation is:
(x, y) -> (x - 8, y + 20)
This means that to apply the translation, we subtract 8 from the x-coordinate and add 20 to the y-coordinate of the original point.
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A truck that can carry no more than 5600 pounds is being used to transport refrigerators an upright pianos it refrigerator weighs 300 pounds in each piano weights 425 pounds write and graph an inequality to show how many refrigerators and how many pianos the truck carry. will nine refrigerators and eight pianos overload the truck?explain.
Since 6100 is greater than 5600, nine refrigerators and eight pianos would overload the truck.
What is linear inequality?
A linear inequality is an equation that represents a linear relationship between two variables and is used to describe a region of the coordinate plane that satisfies a given set of conditions.
Let "x" be the number of refrigerators and "y" be the number of pianos. The total weight of the refrigerators is 300 pounds per refrigerator, so the total weight of the refrigerators is 300x pounds. The total weight of the pianos is 425 pounds per piano, so the total weight of the pianos is 425y pounds. The total weight of the load must be less than or equal to 5600 pounds, so we can write an inequality as follows:
300x + 425y ≤ 5600
To graph this inequality, we can use the coordinates of points that satisfy the inequality and shade the region that represents the solutions.
To determine if nine refrigerators and eight pianos would overload the truck, we can substitute these values into the inequality and see if it still holds:
300 × 9 + 425 × 8 = 2700 + 3400 = 6100
Since 6100 is greater than 5600, nine refrigerators and eight pianos would overload the truck.
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I need another answer asap! Please and thank you if you answer this and you will get 15 points! So what is the answer to this question? Dax is buying coffee for 5
people in his office. He also leaves a $2.00
tip for the barista.
If his total, with tip, is $18.25,
how much is each cup of coffee, not including the tip?
Enter your answer as a decimal, like this: 42.53
Answer:
3.25
Step-by-step explanation:
total 18.25 - 2.00 tip = 16.25
16.25/5=3.25
Landon is buying jerseys for his baseball team. He will pay $11 for each shirt, plus a one-time fee of $30 for the design. Which equation can be used to find y, the total cost to buy x shirts?
Answer:
The equation to find the total cost for buying x shirts would be y = 11x + 30
Step-by-step explanation:
The equation y = 11x + 30 represents the total cost of buying x jerseys, where x is the number of jerseys and y is the total cost. The $11 represents the cost of each jersey and the $30 is the one-time fee for the design. So, for every jersey purchased, the cost goes up by $11, and the $30 fee is added on top of that.
What is the inverse of the function f(x)=5x+7−−−−−√3?
Answer:
The inverse function can be written as:
g(x) = (x - 7 + √3) / 5
Step-by-step explanation:
Starting with the equation y = 5x + 7 - √3, we switch the roles of x and y to get x = 5y + 7 - √3.
Next, we isolate y by subtracting 7 and adding √3 to both sides, which gives x - 7 + √3 = 5y.
Finally, we divide both sides by 5 to get g(x) = (x - 7 + √3) / 5.
This is the inverse function g(x) of f(x) = 5x + 7 - √3. The inverse function is useful in solving problems where the original function is not explicitly invertible.
If a² + a -½= 5 and a½ - a½ >0, calculate the value of (1) a+a¹
Answer:
we can find a + a^(1/2) by substitution:
a + a^(1/2) = 6/5 + √(6/5)
Step-by-step explanation:
We have the equation:
a² + a - 1/2 = 5
Adding 1/2 to both sides:
a² + a = 5 1/2
Factoring out a from the left-hand side:
a(a + 1) = 5 1/2
Taking the square root of both sides:
a + 1/2 = ±√(5 1/2 / a)
Since a^(1/2) - a^(1/2) > 0, we know that a is positive, so we can discard the negative root. Then we have:
a + 1/2 = √(5 1/2 / a)
Squaring both sides:
a² + a + 1/4 = 5 1/2 / a
Substituting the expression for a² + a from the first equation:
5 1/2 - 1/2 + 1/4 = 5 1/2 / a
Multiplying both sides by a:
5 1/2 a - 1/2 a + 1/4 a = 5 1/2
Simplifying:
5a - 1/2 = 5 1/2
Adding 1/2 to both sides:
5a = 6
Dividing by 5:
a = 6/5
Finally, we can find a + a^(1/2) by substitution:
a + a^(1/2) = 6/5 + √(6/5)
ANSWER PLEASE 10 POINTS!!! EXPLANATION INCLUDED TOO PLS!
There are red tiles and blue tiles in a box. the ratio of red tiles to blue tiles is 3:5. There are 12 more blue tiles than red tiles in the box. How many red tiles are in the box?
Ty!
r = red tiles
b = blue tiles
b = r + 12 , whatever "r" is, "b" is 12 more than that
[tex]\stackrel{red}{3}~~ : ~~\stackrel{blue}{5}\qquad \implies \cfrac{r}{b}=\cfrac{3}{5}\implies \cfrac{r}{r+12}=\cfrac{3}{5}\implies 5r=3r+36 \\\\\\ 2r=36\implies r=\cfrac{36}{2}\implies r=18[/tex]
Answer:
18
Step-by-step explanation:
Because there are 12 more blue tiles than red, that means that we can write the equation 3x + 12 = 5x. By simplifying, the equation is boiled down to 12=2x. By dividing, we see that x=6. This means that we can multiply 3 by 6 to get 18 red tiles. To check our answer, we just multiply 6 by 5 to get 30, and the ratio 18:30 is equivalent to 3:5. Also, 30-18=12, so this must be correct.
Jayden folded a 66 \text{ cm}66 cm66, start text, space, c, m, end text strip of paper into 666 equal parts to model a honeycomb cell. Each part was one side of the model.
What is the length of one side of the model?
The length of one side of the model is 0.099cm/part.After Jayden folded a 66 cm strip of paper into 666 equal parts to model a honeycomb cell.
Jayden created a model of a honeycomb cell by folding a 66 cm strip of paper into 666 equal corridor. By dividing the total length of the strip by the number of corridor.
The length of one side of the model can be calculated as follows:
66 cm / 666 = 0.099 cm/part
Thus,it means each side of the honeycomb cell model is roughly 0.099 cm long. This length was determined by Jayden by dividing the total length of the strip into 666 equal corridor, each part representing one side of the honeycomb cell.
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tyler can type twice as many words wpm as kyla
define variable=
Expression to represent problem=
if kyla can type 3 wpm how many wpm can Tyler type
This means that Tyler can type 6 words in the same amount of time it takes Kyla to type 3 words. This means that Tyler is able to type twice as many words as Kyla per minute.
1. Define a variable
We define a variable called "Tyler" to represent how many words per minute Tyler can type.
2. Write the expression to represent the problem
The expression to represent the problem is "Tyler = 3 * 2", which means that Tyler can type twice as many words per minute as Kyla, who can type 3 words per minute.
The answer is that Tyler can type 6 words per minute, which is twice as many as Kyla can type.
This means that Tyler can type 6 words in the same amount of time it takes Kyla to type 3 words. This means that Tyler is able to type twice as many words as Kyla per minute.
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what percent of 3,000,000 is equal to 3,600,000?
Answer:
120%
Step-by-step explanation:
3,600,000 divided by 3,000,000, times 100 = 120%
So, 120% of 3,000,000 is equal to 3,600,000
Answer:
120 %
Step-by-step explanation:
To solve for this percentage problem, we set up an equation:
[tex]3,000,000 * \frac{x}{100} = 3,600,000[/tex]
[tex]30,000 * x = 3,600,000[/tex]
x = 120
Find the area of the triangle below. Be sure to include the correct unit in your answer. 24 ft 6 ft 15 ft
Answer:
72 [tex]ft^{2}[/tex]
Step-by-step explanation:
a = 1/2(24)(6)
a = 72
Sam's biweekly paycheck is $1500. 1/2 of his paycheck is used to pay bills. 1/5 of his paycheck is deposited into his savings account. The remainder of his paycheck is used for food and entertainment. How much money does Sam have available for food and entertainment?
[tex]\stackrel{\textit{for bills}}{1500\cdot \cfrac{1}{2}}~~ + ~~\stackrel{\textit{for savings}}{1500\cdot \cfrac{1}{5}}~~ + ~~\stackrel{\textit{food and ET}}{x}~~ = ~~\stackrel{total}{1500} \\\\\\ 750+300+x=1500\implies 1050+x=1500\implies x=450[/tex]
notice how using one significant digit would not be graded as correct. given to two significant figures, the current is 2.2 a. does this fall within the 2% tolerance range?
If the current is 2.2 A, it falls within the 2% tolerance range of 2.156 A to 2.244 A and would be considered correct.
To determine if 2.2 A falls within the 2% tolerance range, we first need to establish what the expected current value is. If the expected current value is not specified, it's best to use the maximum rated current value as the expected value.
Once we have the expected current value, we can calculate the tolerance range. Tolerance is expressed as a percentage of the expected value, and in this case, it's 2%.
So the tolerance range is:
(Expected Value) * (Tolerance Percentage) = Tolerance Range
For example, if the expected value is 2.2 A, then the tolerance range would be:
2.2 * 0.02 = 0.044
The tolerance range represents the amount by which the actual current can deviate from the expected value and still be considered acceptable. In this case, the tolerance range is 0.044 A, so the acceptable range for the current would be:
(Expected Value - Tolerance Range) to (Expected Value + Tolerance Range)
2.2 - 0.044 to 2.2 + 0.044 = 2.156 to 2.244
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use cosine rule to find angle BAC
Answer:
where's the figure??
Step-by-step explanation:
i think this question is incomplete
What is the slope of the line shown below?
A. -2
B. -6
C. 2
D. 6
Answer:
Step-by-step explanation:
a-2
Wyatt climbed the stairs to ride the waterslide. The top of the waterslide was a maximum 56 feet from the ground. Which graph represents this inequality?
PLS TELL TRUTH
The graph represents this inequality which has been attached below. The number line with a closed circle on the number 56 and a line shaded to the left.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
The water slide is 56 feet in height. A closed and shaded circle to the left of the graph indicates the inequality x 56.
The graph showing the inequality x 56 on the number line starting at 56 is represented as a closed and shaded circle.
Thus, the required graph has been attached below.
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