Answer:
Step-by-step explanation:
1.3 * 10 ^-7
is 0.00000013
0.00000013 times 15 is
0.00000195.
0.00000195 in scientific notation is
1.95*10^-6
Oliver and Chen both write down a number. Oliver says, my number has 8 hundreds and Chen's number only has 3 hundreds my number must be bigger. Oliver is not correct. explain why
Oliver's number is bigger than that of Chen.
What are hundreds in a number?It is a number equal to 10 times 10.
Given is that Oliver and Chen both write down a number. Oliver says, my number has 8 hundreds and Chen's number only has 3 hundreds, my number must be bigger.
Oliver number can be written as follows -
8 x 10 x 10
Chens number can be written as follows -
3 x 10 x 10
It can be concluded that Oliver's number is bigger than that of Chen.
Therefore, Oliver's number is bigger than that of Chen.
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6. Paul sat on a bench by the river and 30
counted the passing boats. He counted
24 speed boats, 5 sail boats, and 1
rowboat. What is the experimental
probability that the next boat he sees
will be a sailboat
Answer:
The total number of boats Paul counted is 24 speed boats + 5 sail boats + 1 rowboat = 30 boats.
So, the experimental probability that the next boat he sees will be a sailboat is 5 sail boats / 30 boats = 1/6.
The experimental probability of an event is defined as the ratio of the number of times the event occurs to the total number of trials or observations.
In this case, Paul observed a total of 24 + 5 + 1 = 30 boats, of which 5 were sailboats.
Therefore, the experimental probability that the next boat Paul sees will be a sailboat is:
Experimental probability = number of sailboats / total number of boats
Experimental probability = 5 / 30
Experimental probability = 1/6
So the experimental probability of seeing a sailboat next is 1/6 or approximately 0.167.
Write an inequality to represent the following: 75 less than a number x is greater than or equal to 420.
Answer: [tex]x-75\geq 420[/tex]
Step-by-step explanation:
... as it say...
Answer:
x -75 ⩾ 420
Step-by-step explanation:
we take away 75 from the value of X and compare it to 420 using the greater than or equal sign.
In a new study, Dr Matti Uhari and colleagues at the University of Oulu in Finland, randomly gave 857 healthy children in daycare centers xylitol in syrup, gum or lozenge form, or a placebo gum, syrup or lozenge in five doses per day for 3 months. According to a report in the October issue of the Journal of Pediatrics, the incidence of ear infections were reduced by 40% in children given xylitol chewing gum, 30% in those given syrup and 20% in those given lozenges when compared to children give a placebo. a) is this an observational study or a randomized experiment? b)If this is an experiment, what are the 3 criteria in this case? c) What are the explanatory and response variables? d)If it is an experiment, diagram the randomized comparative experiment.
(a) Randomized experiment, (b) There are three criteria for a randomized experiment
a) This is a randomized experiment.
b) The three criteria for a randomized experiment are:
Random assignment, the children were randomly assigned to the xylitol or placebo group.
Control group, a placebo group was used as a control.
Manipulation, the children were given different forms and doses of xylitol or placebo.
c) The explanatory variable is the form and dose of xylitol or placebo given to the children. The response variable is the incidence of ear infections.
d) Diagram of the randomized comparative experiment:
Population of healthy children in daycare centers
↓
Random assignment to xylitol or placebo group
↓
Intervention group: given xylitol in syrup, gum or lozenge form
Control group: given a placebo in gum, syrup or lozenge form
↓
Comparison of incidence of ear infections in intervention and control groups
↓
Analysis of results to determine the effectiveness of xylitol in reducing ear infections.
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HELP PLEASE!! SOLVE 2x=32 IS 2 DIFFERENT WAYS
i know the one way is
2x/2 = 32/2
x= 16
WHAT IS THE OTHER WAY???!!
Answer: 4x = 64 or -32/-2
Step-by-step explanation:
you could multiply both sides by 2.
4x = 64
4x/4 = 64/4
x = 16
OR
-2x or -32 to both sides
-32 = -2x
divide both sides by -2
x = -32/-2
x = 16
hope this helps
Determine the domain and range of the given
function.
The domain is
The range is
domain = all real numbers
range = y > -2
y=x²-2
range is y is -2
domain is x is
Julia bought a total of 52 cans of Dr. Pepper and Sprite. There were three times as many cans of Dr. Pepper as Sprite. How many cans of Dr. Pepper did he buy?
Answer:
Step-by-step explanation:
The number of Dr. Pepper cans are 39.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, Julia bought a total of 52 cans of Dr. Pepper and Sprite.
There were three times as many cans of Dr. Pepper as Sprite.
Let number of sprite cans be x.
Then, the number of Dr. Pepper cans will be 3x.
Now, x+3x=52
4x=52
x=13
So, 3x=39
Therefore, the number of Dr. Pepper cans are 39.
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Evaluate the expression.
(
–
0.3–
–
0.9)÷(
–
0.6–
–
0.5)
Write your answer as an integer or a decimal. Do not round.
The complete question:
Evaluate the expression. 0.3 = -5 - (-0.4 - -0.6) Write your answer as an integer or a decimal. Do not round.
Solution:
The value of the expression in a decimal form is, -17.33.
What are expressions?An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.
For example, 2x+3
We have,
0.3x = -5 - (-0.4 - (-0.6))
0.3x = -5 - (-0.4 + 0.6)
0.3x = -5 - 0.2
0.3x = -5.2
x = -5.2/0.3
x = -17.33
Therefore, the value of x is -17.33.
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Examine the triangle below, solve for t, round to the nearest whole number.
T
37
46°
A
84°
t
D
In the triangle, the nearest whole number of the side t is 28.
What is the sine rule of a triangle?The sine rule states that the ratios of the sides to their corresponding opposite angles are equal to a particular value. This value gives the circumradius of that triangle.
The sum of three angles in a triangle is 180°.
Find the angle ∠T for ∠A=46° and ∠D=84°.
∠A+∠D+∠T=180°
46°+84°+∠T=180°
130°+∠T=180°
∠T=50°
The sine rule for triangle ABC is [tex]\[\frac{a}{{\sin A }} = \frac{{37}}{{\sin B }} = \frac{c}{{\sin C }} = 2R\][/tex], where R is the circumradius and a, b, and c are the opposite sides of the angles ∠A, ∠B, and ∠C, respectively.
On applying the sine rule to triangle ADT, the result becomes [tex]\[\frac{a}{{\sin 46^\circ }} = \frac{{37}}{{\sin 84^\circ }} = \frac{t}{{\sin 50^\circ }} = 2R\][/tex].
Take the equation [tex]\frac{{37}}{{\sin 84^\circ }} = \frac{t}{{\sin 50^\circ }}[/tex] and find t.
[tex]\[\begin{array}{l}t = \frac{{37\sin 50^\circ }}{{\sin 84^\circ }}\\ \approx 28.4997\\ \approx 28\end{array}\][/tex]
Therefore, the nearest round whole number of t is 28.
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(4,−2) and (−8,−1) slope intercept form
In the figure below angle A and angle B make a right angle.
Suppose A = 2x - 8
and L B = 3x + 5.
Given this information the measure of B would be
degrees
The measure of ∠B of the right angle is 152°
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ABC
Now , the measure of ∠A = 2x - 8
The measure of ∠B = 3x + 5
And , angle A and angle B make a right angle
On simplifying the equation , we get
2x - 8 = 90
Adding 8 on both sides of the equation , we get
2x = 98
Divide by 2 on both sides of the equation , we get
x = 49
Substitute the value of x in equation , we get
∠B = 3 ( 49 ) + 5
The measure of ∠B = 152°
Hence , the angle is ∠B = 152°
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The temperature in burr town starts at 21 F at midnight when H=0 for the next few hours the temperature drops 4 degrees every hour which equation represents the temperature at hour h
Answer:
t = 21 + (-4)h
Step-by-step explanation:
t = temp. at hour h
h = # of hours past midnight
t = 21° + (-4°/hr)h
Find the total cost to the nearest cent.
$890 computer; 5.5% tax
Please help me !!! I can’t find the answer
Answer:
Based on the measures of the following triangle's angles, the triangle can be classified as an obtuse triangle.
Step-by-step explanation:
In order to decide which type of triangle this is, first we must understand what an acute, right, and obtuse triangle are. Acute triangles are triangles with all three of its angles less than 90°, right triangles are triangles with one angle that is exactly 90°, and obtuse triangles are triangles with one angle that is greater than 90°. Overall, we can determine the type of this triangle by looking at its angles.
The given triangle has the angles 25°, 136°, and 19°. Now we can compare it to the rules above and see whether this triangle is acute, right, or obtuse. As the given triangle has an angle that is greater than 90°, we can conclude that the following triangle is an obtuse triangle.
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Show the work steps for finding the roots of x^4-13x^2+36 algebraically
The factors of given polynomial are (x+3), (x-3), (x+2) and (x-2).
What are factors of polynomial?The factors are the polynomials which are multiplied to produce the original polynomial.
The given polynomial is x⁴-13x²+36
Here, x⁴-13x²+36 can be written as x⁴-9x²-4x²+36
= x²(x²-9)-4(x²-9)
= (x²-9)(x²-4)
= (x²-3²)(x²-2²)
By using the identity a²-b²=(a+b)(a-b)
So, (x+3)(x-3)(x+2)(x-2)
Therefore, the factors are (x+3), (x-3), (x+2) and (x-2).
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Graph the points (0.5,
–
1.5) and (3,5) on the coordinate plane.
The graph of the points on a coordinate plane is added as an attachment
How to graph the points on a coordinate planeFrom the question, we have the following parameters that can be used in our computation:
(0.5, -1.5) and (3,5) on the coordinate plane
The description of the points are:
The point (0.5, -1.5) is located half a unit to the right of the origin and 1.5 units below the origin.The point (3,5) is located 3 units to the right of the origin and 5 units above the origin.Using the above as a guide, we have the graph as an attachment
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The ratio of boys to girls at the park is 4 to 5. How many boys are at the park if there are 45 girls at the park.
Responses
A 30
B 36
C 42
D 48
Answer: Given the ratio of boys to girls at the park is 4 to 5, then there are 4 boys for every 5 girls. If there are 45 girls at the park, then there are 4 * 45 / 5 = 36 boys at the park.
So, the answer is B) 36.
Step-by-step explanation:
What is the y-intercept of y = x^2 - 3x + 2 by completed square form?
y-intercept(s): (0,−2)
Answer:
2
Step-by-step explanation:
The [tex]x^{2}[/tex] and x terms are made to follow the sequence:
[tex][a-b]^{2} =a^{2} -2ab + b^{2}[/tex]
Therefore the [tex]b^{2}[/tex] term has to be added to complete the [tex][a -b]^{2}[/tex] sequence, but at the same time the [tex]b^{2}[/tex] term has to be balanced as it is not originally present in the equation:
[tex]y = x^{2} - 3x + 2 = [(x)^{2} - 2(x)(\frac{3}{2}) + (\frac{3}{2})^{2}] + 2 - (\frac{3}{2})^{2}[/tex]
[tex]= [x - \frac{3}{2}]^{2} + 2 - \frac{9}{4}[/tex]
= [tex][x - \frac{3}{2}]^{2} + \frac{8}{4} - \frac{9}{4}[/tex]
= [tex][x- \frac{3}{2}]^{2} \frac{+ 8-9}{4}[/tex]
= [tex][x-\frac{3}{2}]^{2} -\frac{1}{4}[/tex]
y-intercept is the y-value obtained when x = 0 in the equation:
[tex]= [0 - \frac{3}{2}]^{2} -\frac{1}{4}[/tex]
= [tex](-\frac{3}{2})^{2} -\frac{1}{4}[/tex]
= [tex]\frac{9}{4} - \frac{1}{4}[/tex]
= [tex]\frac{8}{4}[/tex]
= 2
Graph this line:
y+4=3(x-6)
Click to select points on the graph.
104
-10 -8 -6
-4
-2
8
6
4
2
0
-2
4
6
-8
10
3
2
4
6
8
10
The solution is: (A) y+4=-3(x+6), is the equation of the line in point-slope form.
What is slope?In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).
here, we have,
The point-slope form of the equation of a line whose slope is m and passes through the point (x1,y1) is:
y-y1 = m (x-x1)
Given the point:
(x1,y1) = (-6, -4)
Slope, m= -3
x1 = -6,
y1 =-4
Substituting these values into: y-y1 = m (x-x1) , we obtain the point slope form of the equation:
we get,
y+4=-3(x+6)
The correct option is A.
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complete question:
The graph of a line has a slope of -3 and passes through the point (-6,-4).
What is the equation of the line in point-slope form?
Oy + 4 = -3(x + 6)
y + 6 = -3(x + 4)
y-4 = -3(x-6)
y-6 = -3(x – 4)
Question 1
What are the coordinates of the x-intercept and y-intercept of the line
4y-4x= -16.
Question content area top
Part 1
Find the slope of the line if it is defined.
Through (6,5) and (6,-8)
Answer:
undefined or no slope.
Step-by-step explanation:
m is slope. slope is always change of y over change of x. this mean. y2-y1 divide by x2-x1. in this case y2 is -8, y1 is 5 and x2 is 6 and x1 is 6. remember the number in front the variable are base. the answer is undefined.
What is the vertex for the graph?
Answer:(4,-1)
Step-by-step explanation: The vertex is the highest point of the parabola (curved line). The vertex is the point where the parabola crosses its axis of symmetry.
The Function F(T)=575,000/1+4000e^-T describes the number of people, F(T) , who have become ill with ebola T weeks after the initial outbreak in a particular community.
How many people became ill with ebola when the epidemic began?
How many people were infected 6 weeks after the initial breakout? Round to the nearest whole number of people?
What is the limiting size of the infected population? That is, how many people were infected at t = (infinity sign goes after = sign)? Round to the nearest whole number of people.
Step-by-step explanation:
you have to be careful when typing questions and particularly formulae and expressions here. automatic text conversion has the habit of transforming e.g. fractions into one line divisions without any brackets.
what your wrote here :
575,000/1 + 4000e^-T = 575,000 + 4000e^-T
that cannot be the function.
I am sure it must be
F(T) = 575,000/(1 + 4000e^-T)
right ?
I am basing the rest of my answer on that assumption.
how many people became ill, when the outbreak began ? that means T = 0.
F(0) = 575,000/(1 + 4000e^-0) =
= 575,000/(1 + 4000×1) =
= 575,000/(4001) = 143.7140715... ≈ 144 people
6 weeks after the outbreak
F(6) = 575,000/(1 + 4000e^-6) =
= 575,000/(1 + 4000/(e^6)) =
= 575,000/(1 + 9.915008707...) =
= 575,000/10.915008707... =
= 52,679.75642... ≈ 52,680 people
limit t -> infinity
F(infinity) = 575,000/(1 + 4000e^-infinity) =
= 575,000/(1 + 4000/(e^infinity)) =
= 575,000/(1 + 0) = 575,000 people
Alanis is moving and needs to pack two mirrors the largest mirror fits in a box that is 18 inches wide by 20 inches long her smaller mirror is similar in proportion to the larger mirror Alanis determines that the width of the smaller box needs to be a minimum of 9 inches. what should the minimum length of the box to hold the smaller mirror ?
The minimum length of the box to hold the smaller mirror is 10 inches for largest mirror fits in a box that is 18 inches wide by 20 inches long her smaller mirror.
What is proportion ?
In mathematics, proportion refers to the equality of two ratios. Two ratios are said to be proportional if they have the same relative size, meaning they represent the same relationship between quantities.
For example, if we have two ratios, such as 2/3 and 4/6, they are proportional because they represent the same relationship between two quantities. We can say that 2 is to 3 as 4 is to 6, and we can simplify both ratios by dividing the numerator and denominator of each by their greatest common factor, which in this case is 2.
Since the smaller mirror is similar in proportion to the larger mirror, the ratio of their corresponding sides is the same. Therefore, the width of the smaller box is half of the width of the larger box (9 inches is half of 18 inches).
To find the minimum length of the smaller box, we need to use the same ratio of sides. The length of the larger box is 20 inches, so the length of the smaller box should be half of 20 inches, which is 10 inches.
Therefore, the minimum length of the box to hold the smaller mirror is 10 inches.
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The table shows the number of 6th grade students who prefer each kind of juice at lunch time. Draw a circle graph to display the information. 6th Grade Juice Choices: Grape Juice 8, Orange Juice 6, Fruit Punch 6, Apple Juice 20.
A circle graph representing the data presented will show half of the students prefer apple juice; while grape, orange juice, and fruit punch are preferred by a lower ratio of students.
What is a circle graph?A circle graph also known as a pie graph is a visual representation of data based on a circle and its fractions of it. In this way, if 20 out of the 40 students prefer apple juice this means in the circle graph half of it would be for students preferring apple juice.
Based on this, a possible circle graph that represents the data is shown below:
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This question is due today. Could someone possibly help me.
Applying the triangle proportionality theorem, QR = 17½.
What is the Triangle Proportionality Theorem?The triangle proportionality theorem states that when a line is constructed parallel to one side of a triangle and intersects the remaining two sides at two different points, the two sides of the triangle will be divided in equivalent proportions.
Therefore:
SQ/PS = TQ/TR
SQ = 5
PS = 2
TQ = ?
TR = 5
Plug in the values:
5/2 = TQ/5
Cross multiply:
2TQ = 25
TQ = 25/2
TQ = 12½.
QR = TQ + TR
QR = 12½ + 5
QR = 17½
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In planning for a new forest road to be used for tree harvesting, planners must select the location that will minimize tractor skidding distance. In order to estimate the true mean skidding distances along a new road in a European forest, skidding distances (in meters) were measured at 20 randomly selected road sites. The data are shown in the following table.
In planning for a new forest road to be used for t
a. Calculate the mean, variance, and standard deviation of this sample.
b. Estimate the true mean skidding distance of the road with a 95% confidence interval.
c. What assumptions are needed for your inference in (b) to be valid? How would you check them?
d. A logger working on the road claims that the mean skidding distance is at least 425 meters. Do you agree? Why?
The mean, variance, and standard deviation of this sample is 377.5, 7007.5 meters^2 and 83.7 metres respectively. The 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters. we find that the p-value for a t-statistic of -3.61 is less than 0.01.
To calculate the mean, variance, and standard deviation of this sample, we can use the following formulas:
Using the formulas, we get:
Mean = (365 + 350 + 380 + 400 + 395 + 375 + 385 + 380 + 390 + 370 + 360 + 370 + 380 + 370 + 400 + 385 + 375 + 385 + 380 + 375) / 20
= 377.5 meters
Variance = [(365-377.5)^2 + (350-377.5)^2 + (380-377.5)^2 + ... + (380-377.5)^2 + (375-377.5)^2] / (20-1)
= 7007.5 meters^2
Standard deviation = square root of variance = sqrt(7007.5) = 83.7 meters
Therefore, the mean skidding distance is 377.5 meters, the variance is 7007.5 meters^2, and the standard deviation is 83.7 meters.
To estimate the true mean skidding distance of the road with a 95% confidence interval, we can use the following formula:
Confidence interval = sample mean ± (t-value * (standard deviation / sqrt(sample size)))
Here, the sample mean is 377.5 meters, the standard deviation is 83.7 meters, and the sample size is 20. To find the t-value, we need to look it up in a t-distribution table with 19 degrees of freedom. From the table, we find that the t-value for a 95% confidence interval is 2.093.
substituting the values, we get:
Confidence interval = 377.5 ± (2.093 * (83.7 / sqrt(20)))
= 377.5 ± 37.0
Therefore, the 95% confidence interval for the true mean skidding distance is (340.5, 414.5) meters.
The assumptions needed for this inference to be valid are:
The sample is a random sample from the population of skidding distances along the road.
The skidding distances follow a normal distribution in the population.
The sample size is large enough (at least 30) or the population standard deviation is known.
To check these assumptions, we can use a normal probability plot to check for normality and calculate the sample size to see if it is large enough. We can also use previous studies or expert knowledge to check if the assumption of normality is reasonable.
To test the logger's claim that the mean skidding distance is at least 425 meters, we can perform a one-sample t-test. The null hypothesis is that the mean skidding distance is 425 meters, and the alternative hypothesis is that it is less than 425 meters.
Using the formula for the t-statistic, we get:
t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))
= (377.5 - 425) / (83.7 / sqrt(20))
= -3.61
From a t-distribution table with 19 degrees of freedom, we find that the p-value for a t-statistic of -3.61 is less than 0.01. Therefore, we reject the null hypothesis and can conclude that there is not enough evidence to support the logger's claim. Therefore, we do not agree with the logger's claim.
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Find the range of each set of data.
Set 1: 1, 4, 6, 8, 10, 12
Range =
Set 2: 230, 24, 33, 22, 41
Range =
Which set of data has a wider spread of data?
The range of set 1 is 11. The range of set 2 is 208
The wider range of set 2, set 2 contains a wider spread of the given data.
What is the range of the data?The range of the data is defined as the difference between the maximum value of data and the minimum value of the data.
The set is given in the question, as follows:
Set 1: 1, 4, 6, 8, 10, 12
The maximum value = 12
The minimum value = 1
The range of the set 1 = maximum value - minimum value
Substitute the values in the above formula,
The range of the set 1 = 12 - 1
Apply the subtraction operation to get the answer
The range of the set 1 = 11
Set 2: 230, 24, 33, 22, 41
Now, the range of the set 2 = 230 - 22 = 208
Data set 1 has a range of 11, whereas data set 2 has a range of 208.
Therefore, the wider range of set 2, set 2 contains a wider dispersion of data.
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A 15.5-m fire truck ladder is leaning against a wall. Find the distance d the ladder goes up the wall (above the fire truck)if the ladder makes an angle of 53° 25' with the horizontal
d= ? m
The distance the ladder goes up the wall is approximately 12.14 meters.
What is trigonometry ?
Trigonometry is a branch of mathematics concerned with relationships between angles and ratios of lengths.
We can use trigonometry to solve this problem.
Let's call the distance the ladder goes up the wall "d". We can use the angle the ladder makes with the horizontal to find the length of the ladder that is leaning against the wall.
We know that the ladder is 15.5 m long, so we can use the sine function to find the length of the ladder that is leaning against the wall:
sin(53° 25') = d/15.5
We can solve for "d" by multiplying both sides by 15.5:
d = 15.5 * sin(53° 25')
Using a calculator, we get:
d ≈ 12.14 m
Therefore, the distance the ladder goes up the wall is approximately 12.14 meters.
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I’m stuck on this one question help
Answer:
E is a major arc
C is a minor sector
A is a major segment
Major segment is the portion (or part) of the circular region enclosed between a chord and the corresponding major arc.
Major arc is the longer arc connecting two endpoints on a circle.
A sector with a central angle less than 180° is called a minor sector.
