In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
To find the annual rate of change between 1992 and 2006, we can use the formula:
r = [tex](V_2/V_1)^{1/n}-1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.
=>r = -0.0839
Therefore, the rate of change between 1992 and 2006 is -0.0839.
To express the rate of change in percentage form, we can multiply the result from part A by 100:
=>r = -0.0839 x 100
=> r = -8.39%
Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.
To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.
From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:
where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.
=>V = 11792.51
Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).
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r=-0.49 and the margin of error for 95% confidence is 0.10
Answer:
Step-by-step explanation:
um
Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options. 5(x2 + 4x + 4) = –7 + 20 x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot 5(x2 + 4x) = 7 5(x2 + 4x + 4) = 7 + 20 5(x2 + 4x) = –7
The solutions to the quadratic equation [tex]5x^2 + 20x - 7 = 0[/tex] are[tex]x = -2 + \sqrt{(23/5)[/tex] and [tex]x = -2 - \sqrt{(23/5)[/tex].
A quadratic equation is a second-degree polynomial equation of the form [tex]ax^2 + bx + c = 0[/tex], where x is the variable, and a, b, and c are coefficients, where a is non-zero.
The square root is an important mathematical concept that arises in many areas of mathematics and science, such as geometry, algebra, and physics. It is used to calculate the length of sides of a right triangle, to solve quadratic equations, and to model the behavior of physical systems
The three steps Sergey could use to solve the quadratic equation by completing the square are:
Rewrite the equation in the form [tex]ax^2 + bx + c = 0[/tex].
Add and subtract [tex](b/2a)^2[/tex] to complete the square:
[tex]5(x^2 + 4x + 4 - 4) = 7[/tex]
Simplify the left side and solve for x by taking the square root:
[tex]5(x + 2)^2 = 11[/tex]
[tex](x + 2)^2 = 11/5[/tex]
[tex]x + 2 = \pm \sqrt{(11/5)[/tex]
[tex]x = -2 \pm \sqrt{(11/5)[/tex]
Therefore, the three correct options are:
[tex]5(x^2 + 4x + 4 - 4) = 7[/tex]
[tex]5(x + 2)^2 = 11[/tex]
[tex](x + 2)^2 = 11/5, x = -2 \pm \sqrt{(11/5)[/tex]
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calculo del incremento %
se tiene 5430 y se gasto 1150
¿que porcentaje de dinero se gasto?
PLS SOMEONE HELP MEEEEE
In conclusion MN is approximately 8.73.
How to solve?
In triangle MNK, we know that MN = NK and the angle between them is 110 degrees. Let's call the third angle in this triangle A.
We also know that MK = 5.
Since the sum of the angles in a triangle is always 180 degrees, we can find angle A:
A + 110 + A = 180
2A = 70
A = 35
Now we can use the Law of Sines to find MN:
MN/sin(110) = MK/sin(A)
MN/sin(110) = 5/sin(35)
MN = 5×sin(110)/sin(35)
MN ≈ 8.73
Therefore, MN is approximately 8.73.
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Complete Quedtion:
In triangle AMNK, we have MN = NK, angle M/N = 110 degrees, and MK = 5. What is the length of MN?
A randomized comparative experiment tests whether a cholesterol medication lowers the overall blood pressure for male patients. The control group has ten male patients and the treatment group, which receives the medication, has 10 male patients. All patients started with a cholesterol level of 245 mg/dL. Cholesterol in mg/dL Control 241 243 242 245 250 248 246 245 242 247 Treatment 230 225 220 218 224 240 232 221 235 224 What is the difference in the treatment mean and control mean
Therefore, we can't calculate the difference in blood pressure between the control and treatment groups. Difference in means: 244.9 - 226.5 = 18.4 mg/dL.
by the question.
The question appears to be incomplete. It asks for the "difference," but it doesn't specify what difference it's referring to. Based on the information provided, I can provide some possible interpretations and calculations:
Difference in cholesterol levels before and after treatment:
Since all patients started with a cholesterol level of 245 mg/dL, we can't calculate the difference in cholesterol levels before and after treatment. We don't have any data on the patients' cholesterol levels after treatment.
Difference in average cholesterol levels between the control and treatment groups:
Control group mean: (241+243+242+245+250+248+246+245+242+247)/10 = 244.9 mg/dL
Treatment group mean: (230+225+220+218+224+240+232+221+235+224)/10 = 226.5 mg/dL
Difference in means: 244.9 - 226.5 = 18.4 mg/dL
Difference in average blood pressure between the control and treatment groups:
The prompt states that the experiment tested whether the cholesterol medication lowers the overall blood pressure for male patients, but it doesn't provide any data on blood pressure.
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there us 40 pens 9 out of 10 r black wats the fraction an the percentage
Answer:
White
Step-by-step explanation:
Number of favorable outcomes/Number of trails =4/20 or 1/5
Explain how you would organize your step-by-step calculations in evaluating the order of operations problem below. (Remember PEMDAS!) There should be five steps in this calculation. For full credit you must provide a step-by-step explanation as well as computation for the correct answer.
8÷2 (1+3) - 2^3
The steps that should be taken to evaluate the order of operations given are:
Solve for the brackets Solve for the exponents Solve the division Multiply by the result of the bracket Subtract the result of the exponents How to solve with PEMDAS ?To solve with PEMDAS, you first need to solve what is in the brackets in the order of operations given which is 8÷2 (1+3) - 2^3.
= 8÷2 (1+3) - 2^3
= 8÷2 x 4 - 2^3
Then solve for the exponents :
= 8÷2 x 4 - 2^3
= 8÷2 x 4 - 8
Then because the division comes first, you solve for that:
= 8÷2 x 4 - 8
= 4 x 4 - 8
You then solve for the multiplication as this takes precedence over subtraction:
= 4 x 4 - 8
= 16 - 8
Then solve the subtraction:
= 16 - 8
= 8
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A street that is 186 m long is covered in snow. City workers are using a snowplow to clear the street. A tire on the snowplow has to turn 31 times in traveling the length of the street. What is the diameter of the tire? Use the value 3.14 for PI . Round your answer to the nearest tenth. Do not round any intermediate steps.
Answer:
The number of times the tire will have to turn in travelling the length of the street is 30.9 times.
To determine the number of times the tire will have to turn in travelling the length of the street, we will first calculate the circumference of the tire.
Since the tire is circular, the circumference of the tire can be calculated from the formula for calculating the circumference of a circle.
The circumference of a circle is given by
C = πd
Where C is the circumference and d is the diameter
From the question d = 1.7m and π = 3.14
∴ C = 3.14 × 1.7
C = 5.338 m
Therefore, the circumference of the tire is 5.338 m
Now, for the number of times the tire will have to turn in travelling the length of the street, we will divide the length of the street by the circumference of the tire.
Number of times the tire will have to turn = Length of the street ÷ Circumference of the tire
Number of times the tire will have to turn = 165 m ÷ 5.338 m
Number of times the tire will have to turn = 30.91045 times
Number of times the tire will have to turn ≅ 30.9 times
Hence, the number of times the tire will have to turn in travelling the length of the street is 30.9 times
A regular tube of toothpaste costs $2.50 for 3.2 ounces. A travel-size tube costs $1.00 for 1.2 ounces. Compare the prices and weights using percent to decide which is the better buy.
Answer: The regular tube is the better buy
Step-by-step explanation: $2.50/3.2 ounces equals $.78 per ounce. $1.00/1.2 ounces equals $.83 per ounce. Therefore, the regular tube is the better buy.
All AABC is reflected across the x-axis, then rotated 90° clockwise about the origin, and finally reflected across the line y = The coordinates of vertex A' are (1, 1) v V The coordinates of vertex B' are (2, 3) The coordinates of vertex C' are|| (2, 1) ********* showing answers i got off here ughh in pic wrong ones
The coordinates of vertex A' are (1, 1)
The coordinates of vertex B' are (2, 3).
The coordinates of vertex C' are (2, 1).
What is a reflection over the x-axis?In Geometry, a reflection over or across the x-axis is represented or modeled by the following transformation rule (x, y) → (x, -y). This ultimately implies that, a reflection over or across the x-axis would maintain the same x-coordinate (x-value) while the sign of the y-coordinate (y-value) changes from positive to negative or negative to positive as the case may be.
In this exercise, you are required to apply a reflection over the x-axis, a rotation of 90° clockwise about the origin, and finally reflected across the line y = x as shown in the transformation table below;
Original vertex Reflection (x-axis) Rotated 90° clockwise Line y = x
A (1, 1) → (1, -1) → (-1, -1) → (1, 1)
B (2, 3) → (2, -3) → (-3, -2) → (2, 3)
C (2, 1) → (2, -1) → (-1, -2) → (2, 1)
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Consider the three sets: A = {2, 4, 6, 8}, B = {1, 3, 5, 7}, and C = {2, 3, 6, 7}. What is the intersection D of these sets? If the intersection is null, then what changes to the set will make the intersection set D = {2}
The new set B = {1, 2, 3, 5, 7}, and the intersection of A, B, and C would be D = {2}.
What is intersection?Intersection is the point at which two sets of data meet. It is the common point or element that exists in both sets.
The intersection of the three sets A, B, and C is the set of elements that are common to all three sets.
In this case, the intersection of A, B, and C is the null set, denoted as ∅. This means that there are no elements that are common to all three sets.
To make the intersection set D = {2}, one of the sets must contain the element 2.
In this case, set A already contains the element 2, so it is sufficient to add the element 2 to one of the other sets, either set B or set C.
Let's say we add the element 2 to set B. The new set would be B = {1, 2, 3, 5, 7}, and the intersection of A, B, and C would be D = {2}.
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Joanne will plant 40 flowers per sq metre of space she will plant 4 x as many red flowers than white
Answer:
7s
Step-by-step explanation:
Joanne ate the flowers and the red flowers tooFind the area of the shaded triangle or quadrilateral.
What is the area of the WAVE
Answer:
Step-by-step explanation:
What is a rectangular prism?
A right rectangular prism is a box-shaped object, that is, a 3-dimensional solid which has six rectangular faces. Rectangular prisms can also be oblique - leaning to one side - but the side faces are parallelograms, not rectangles. A right rectangular prismz is also called a cuboid, box, or rectangular hexahedron. Moreover, "rectangular prism" and "right rectangular prism" are often used interchangeably.
The most common math problems related to this solid are of the type right rectangular prism calc find V or find A, where the letters stand for the Volume and Area, respectively. Let's see the necessary rectangular prism formula and learn how to solve those problems quickly and easily.
How do I find the volume of a rectangular prism?
The rectangular prism volume formula is:
volume = h × w × l,
where h is prism height, w is its width, and l is its length. To calculate the volume of a cardboard box:
Find the box length. For example, it can be equal to 18 in.
Determine its width. Let's say you measured 12 in.
Find out the rectangular prism height. Assume it's 15 in.
Calculate the cuboid volume. Using the rectangular prism volume formula above, we get volume = (18 × 12 × 15) in = 3240 in³.
How do I find the area of a rectangular prism?
The surface area of the cuboid consists of 6 faces - three pairs of parallel rectangles. To find the rectangular prism surface area, add the areas of all faces:
surface_area = 2 × (h × w) + 2 × (h × l) + 2 × (l × w) = 2 × (h × w + h × l + l × w),
where h is prism height, w is its width, and l is its length.
Let's see an example of how to solve the right rectangular prism calc - find A problem. We'll come back to our example with the box and calculate its surface area:
Calculate the rectangular prism surface area. First rectangle area is 15in × 12in = 180in², second 15in × 18in = 270in² and third one 18in × 12in = 216in². Add all three rectangles' areas - it's equal to 666 in² (what a number!) - and finally multiply by 2. The surface area of our cardboard box is 1332in².
Or save yourself some time and use our rectangular prism calculator.
Finally, let's attack the right rectangular prism calc find d (that is, the diagonal) type of problem.
How do I calculate the diagonal of a rectangular prism?
To determine the diagonal of a rectangular prism, apply the formula:
diagonal = √(l² + h² + w²)
where h is prism height, w is its width, and l is its length.
Bilquis is deciding between two different movie streaming sites to subscribe to. Plan A costs $22 per month plus $1 per movie watched. Plan B costs $14 per month plus $3 per movie watched. Let A represent the monthly cost of Plan A if Bilquis watches x per month, and let B represent the monthly cost of Plan B if Bilquis watches x movies per month. Graph each function and determine the interval of movies watched, x, for which Plan A is cheaper than Plan B.
We can express this interval using set-builder notation as: {x | x > 4}
What is expression?
An expression consists of one or more numbers or variables along with one more operation.
The monthly costs of each plan as functions of the number of movies watched:
A(x) = 22 + x
B(x) = 14 + 3x
To graph these functions, we can plot several points for each one, as shown in follow fig.
A(x) - B(x) < 0
(22 + x) - (14 + 3x) < 0
22 + x - 14 - 3x < 0
-2x + 8 < 0
-2x < -8
x > 4
Therefore, Plan A is cheaper than Plan B for any number of movies watched greater than 4. We can express this interval using set-builder notation as: {x | x > 4}
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The Question is in the picture
Using compound interest, we can find that at age 59 retirement option 1 will be better than retirement option 2.
Define compound interest?Compound interest is computed on the principal and the accrued interest for a given time period. The interest that has accumulated on the principal over time is added to it, and the combined amount acts as the new principal for the subsequent time period. Once more, the interest for the following period is calculated using the total cumulative principal amount.
Compound interest is the term used to describe the method of computing interest employed in all financial and business transactions globally. The benefit of compounding is that it is consistently better than or comparable to other strategies, such simple interest.
At age 59,
Option 1 = 30000 × 34
= $1020000
Option 2 = 15000 (1+12/408) ^34
= 15000 × (1.02) ^34
= 15000 × 1.9606
= $29409.
So, when you retire at 59, option 1 is better than option 2.
At age 69,
Option 1 = 30000 × 44
= $1,320,000
Option 2 = 15000 (1+12/528) ^44
= 15000 × (1.02) ^44
= 15000 × 2.390
= $35,850.
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At age 59, retirement option 1 will outperform retirement option 2, according to compound interest.
Define compound interest?On the principal and the interest that has accrued over a specific length of time, compound interest is calculated. The principal is increased by the interest that has accrued on it over time, and the combined sum serves as the new principal for the term that follows. Once more, the entire cumulative principal amount is used to determine the interest for the upcoming period.
The term "compound interest" refers to the technique of calculating interest used in all financial and commercial transactions worldwide. Compounding has the advantage of constantly outperforming or being on par with other approaches, like simple interest.
At age 59,
Option 1:
= 30000 × 34
= $1020000
Option 2:
[tex]=15000(\frac{1+12}{408} )^{34} \\\\=15000\times 1.02^{34}[/tex]
= 15000 × 1.9606
= $29409.
So, when you retire at 59, option 1 is better than option 2.
At age 69,
Option 1:
= 30000 × 44
= $1,320,000
Option 2:
[tex]=15000(\frac{1+12}{528} )^{44} \\\\=15000\times 1.02^{44}[/tex]
= 15000 × 2.390
= $35,850.
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What is the probability of Meikel wearing khakis and sandals?Help.
3/21
1/4
4/8
1/2
Step-by-step explanation:
The probability of Meikel wearing khakis and sandals is
3 ÷ 12 which will give us
1/4
-8^2÷(-2)^3 without using a calculator
Answer:
Step-by-step explanation:
-8^2 and (-2)^3 are exponents so it should be solved first
-8^2 = -64 and (-2)^3 = -8
(-64)/(-8)
64/8
8
8
EXPLANATION:To solve this expression, we need to follow the order of operations, which is PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction) from left to right:
First, we need to simplify the exponents: -8^2 means -1 times 8 squared, which is -1 times 64 or -64. (-2)^3 means -2 multiplied by itself three times, which is -2 x -2 x -2 or -8.
Next, we need to perform the division and multiplication, again from left to right: -64 ÷ -8 equals 8.
Therefore, the final answer to the expression -8^2÷(-2)^3 is 8.
Please help me solve the question!
The probability of winning the minimum award in the lottery is 0.00185%.
What is probability?The possibility of an event occurring is expressed in terms of probability and odds. Probability is often stated as a decimal or percentage and represents the ratio of the number of likely outcomes to all conceivable possibilities. Conversely, odds are often stated as a ratio or fraction and are the ratio of the number of favourable events to the number of negative outcomes.
The probability of correctly matching two out of five white balls is given by the combination formula:
C(5,2) = 5! / (2! * (5-2)!) = 10
The probability of matching the gold ball is = 1/44.
Multiplying we have:
P(win minimum award) = (10 / C(54,5)) * (1 / 44) = 0.0000185, or approximately 0.00185%
Hence, the probability of winning the minimum award in the lottery is 0.00185%.
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Curious about people's recycling behaviors, Sandra put on some gloves and sifted through some recycling and trash bins. She kept count of the plastic type of each bottle and which bottles are properly dispensed.
What is the probability that a randomly selected bottle is correctly placed AND is a Plastic #4 bottle?
show all steps
On solving the provided question we can say that Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.
Therefore there are 15 bottles that match both requirements (well arranged and Plastic #4).
The sample has 100 bottles in total.
As a result, the likelihood that a randomly chosen bottle is appropriately put AND is a Plastic #4 bottle is:
P(properly positioned and Plastic #4) = the number of bottles that match both requirements. / The sample's total number of bottles
P(properly positioned and Plastic #4) = 15 / 100
P(properly positioned and Plastic #4) = 0.15 or 15%
Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.
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(SBAC Performance Task Practice Test Question) Label the dimensions of the net for the current cereal box with dimensions of 12 inches high, 8 inches wide, and 2 inches deep. (Please show how to do it because im at a loss at the time this is being asked)
The dimensions of the net will be the same as the dimensions of the rectangular prism, since the net is just a flattened version of the 3D shape.
What is Rectangular prism ?
A rectangular prism is a three-dimensional geometric shape that has six faces, all of which are rectangles.
To label the dimensions of the net for the current cereal box, you need to identify the six faces of the rectangular prism that makes up the cereal box.
Start by drawing a rectangular prism with the given dimensions (12 inches high, 8 inches wide, and 2 inches deep).
Then, label each face with its dimensions, as follows:
The top face (which will be the same size as the bottom face) has dimensions 8 inches by 2 inches.
The front and back faces have dimensions 12 inches by 8 inches.
The left and right faces have dimensions 12 inches by 2 inches.
Top face: 8 in. x 2 in.
Front and back faces: 12 in. x 8 in.
Left and right faces: 12 in. x 2 in.
Therefore, Note that the dimensions of the net will be the same as the dimensions of the rectangular prism, since the net is just a flattened version of the 3D shape.
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Find the area of a rectangular park whose perimeter is 320m and length is 90m.
First, 90 + 90 = 180
Second, 320 - 180 = 140
Third, 140 / 2 = 70.
| 90 * 70 = 6,300
|
|
| 90
|
|____________
70
Solve the following inequality.
Negative one-half p less-than negative 16
Which graph shows the correct solution?
A number line going from 27 to 37. An open circle is at 32. Everything to the right of the circle is shaded.
A number line going from 27 to 37. An open circle is at 32. Everything to the left of the circle is shaded.
A number line going from 3 to 13. An open circle is at 8. Everything to the left of the circle is shaded.
A number line going from 3 to 13. An open circle is at 8. Everything to the right of the circle is shaded.
After answering the prοvided questiοn, we can cοnclude that As a result, the sοlutiοn tο the inequality is p greater than 32.
What is inequality?In mathematics, an inequality is a nοn-equal relatiοnship between twο expressiοns οr values. As a result, imbalance leads tο inequality. In mathematics, an inequality cοnnects twο values that are nοt equal. Inequality is nοt the same as equality. When twο values are nοt equal, the nοt equal sign is cοmmοnly used ().
Different inequalities, nο matter hοw small οr large, are used tο cοntrast values. Many simple inequalities can be sοlved by mοdifying the twο sides until οnly the variables remain. Hοwever, a number οf factοrs cοntribute tο inequality: Negative values are divided οr added οn bοth sides. Exchange left and right.
We must isοlate the variable p οn οne side οf the inequality sign in οrder tο sοlve it.
-16 negative οne-half p
When bοth sides οf the inequality are multiplied by -2 (and the inequality sign is reversed because we are multiplying by a negative number), we get:
p > 32
As a result, the sοlutiοn tο the inequality is p greater than 32.
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how did they get this answer
Step-by-step explanation:
r = 250 ( thousand) and r = 180 + 35 log4 (x) <====base 4 LOG
sooooo 250 = 180 + 35 log4(x) find 'x' thousands
(250 -180)/35 = log4 (x)
2 = log4(x) these are exponents of 4 ...anti log base 4:
4^2 = 4^(log4 x)
16 = x
But x is thousands of $ (per the question info)
so $ 16 000
Rewrite each equation without absolute value for the given conditions.
y = |x3| + x +2|-|x - 5| if 3
Rewriting the absolute value problems gives us: y = |x − 3| + |x + 2| − |x − 5| = 3 - x + x + 2 - (5 - x) = x
How to write Absolute Value equations?The absolute value is simply defined as the distance from zero.
The equation we are to rewrite is:
y = |x − 3| + |x + 2| − |x − 5|, if -2 < x < 3
Modulus value means that it always gives positive value. Thus:
if x < a, then |x - a| is positive when |x - a | = a -x, which is positive as a is larger than x.
and if x >a, then |x-a| is positive when |x-a| = x - a, which is positive as a is smaller than x.
Applying the same,
For -2 < x < 3,
|x - 3 | = 3 - x, as x <3
| x + 2 | = | x - (-2)| = x - (-2) = x+2 as x> -2
| x - 5 | = 5 -x , as x < 5
Therefore, y = |x − 3| + |x + 2| − |x − 5| = 3 - x + x + 2 - (5 - x) = x
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Solve. (Easy 10 points)
Answer:
A) -3
Step-by-step explanation:
To remove the radical on the left side of the equation, cube both sides of the equation.
[tex]\sqrt[3]{4x + 4}^{3}[/tex] = (-2)³
Simplify each side of the equation.
4x + 4 = -8
4x = -12
x = -3
So, the answer is A) -3
Please Help Solve this Useing the Solve Method, or read what it says and you'll know how to awnser it.
The ratio means that for every 2 motor boats, there are 3 sail boats. 6 sail boats must also enter so that the ratio remains the same. A possible missing information will be the total number of ships in the armada.
What is a ratio?A ratio is a mathematical expression that represents the relationship between two quantities or numbers. It is a comparison of two numbers, often written in the form of a fraction or with a colon. Ratios are used to express how much of one thing there is in relation to another.
1. a. The ratio of motor boats to sail boats can be written in three ways:
As a fraction: 2/3
With a colon: 2:3
With the word "to": 2 to 3
This ratio means that for every 2 motor boats, there are 3 sail boats. Alternatively, it can be interpreted as for every 3 sail boats, there are 2 motor boats. The ratio does not specify the total number of boats, only the relative proportion of motor boats to sail boats.
b. To keep the ratio between motor boats and sail boats the same, we need to maintain the same ratio of motor boats to sail boats.
Currently, the ratio of motor boats to sail boats is 2:3.
Let x be the number of sail boats needed to maintain the ratio.
After x sail boats enter, the total number of boats will be 2 + x motor boats and 3 + x sail boats.
The ratio of motor boats to sail boats will still be 2:3, so we can write,
[tex]\frac{(2 + x)}{(3 + x)}[/tex] = [tex]\frac{2}{3}[/tex]
Cross-multiplying, we get,
2(3 + x) = 3(2 + x)
6 + 2x = 6 + 3x
x = 6
Therefore, 6 sail boats must also enter so that the ratio remains the same.
2. To find the total number of galleons and galleys in the Spanish armada, we need at least one additional piece of information. The ratio of 5:1 tells us that for every 5 galleons, there is 1 galley. However, we don't know the total number of galleons and galleys in the armada.
One possible missing information that could help us find the total number of galleons and galleys is the total number of ships in the armada. If we knew the total number of ships, we could find the number of galleons and galleys in the armada.
For example, let's say the total number of ships in the armada is 100. And let number of galleons = a and number of galleys = b. Then,
a + b = 100
[tex]\frac{a}{b}[/tex] = 5/1
b = a/5
Substituting this expression into the first equation, we get:
a+ (a/5) = 100
(6a/5) = 100
a = 500/6 ≈ 83.33
Then b = (1/5)(83.33) = 16.67
However, since we cannot have a fractional part of a ship, we can round up or down to get whole numbers. Therefore, we can conclude that the Spanish armada had approximately 83 galleons and 17 galleys, based on the given ratio of 5:1.
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will give brainliest if both questions are answered
Answer:
17) x = 23;18) x = 30.------------------------------
Question 17Angle with the measure of 130° forms a vertical angle pair with the sum of x and 107° angle.
Since vertical angles are congruent we have:
x + 107 = 130x = 23Question 18The two angles, x and 2x together form a right angle, since they form a linear pair with another angle, marked as right angle. Therefore, x and 2x are complementary angles:
x + 2x = 903x = 90x = 30The volume of a cone is equal to the volume of a sphere.
The radius of the cone is four times the radius of the sphere.
Write down an expression for h
in terms of r.
You must simplify your answer.
h=
an expression for height h in terms of radius r, h=r/4
Definition of VolumeThe quantity of space a three-dimensional solid shape takes up is measured by its volume. Although it is hard to conceive in any shape, it may be likened to shapes. A compass box, for instance, has a bigger volume than an eraser inserted inside of it.
Volume of Sphere=4/3πr³
Volume of Cone=1/3πR²h
Given:
A cone's volume is equal to a sphere's volume. The cone's radius is four times greater than the sphere's radius.R=4r
4/3πr³=1/3πR²h
4r³=R²h
4r³=(4r)²h
r=4h
an expression for height h in terms of radius r, h=r/4.
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A 56° B D M E What is the value of y? needs an answer asap
Step-by-step explanation:
The inscribed angle BAD = 1/2 arc BD
56° = 1/2 BD
arc BD = 112°
and arc BAD would then be 360 - 112 = 248°
For the EXTERNAL angle y
y = 1/2 ( difference of intercepted arcs ) = 1/2 ( 248 -112)° = 68°
The points (-5, 6) and (x, 3) are elements of an inverse variation.
What is the value of X?
X=-10 when the points (-5, 6) and (x, 3) are elements of an inverse variation.
What is inverse variation?A relationship between two variables known as an inverse variation occurs when one variable increases while the other decreases, resulting in a constant product. Y = k/x, where k is a constant of variation, can be used to explain the relationship between two variables x and y if they are inversely proportional in mathematics.
The fact that their product must be constant allows us to determine the value of x because the points (-5, 6) and (x, 3) are components of an inverse variation.
As a result, x must be 10 to provide the elements of an inverse variation (-5, 6) and (x, 3).
x * 3 = -5 * 6
x = -30/3
x = -10
In conclusion, an inverse variation is a mathematical connection where the product of two variables stays constant.
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