Find the value of x. (Hint: The sum of the angle measures of a quadrilateral is 360°)
X= (simplify your answer)
Answers
Answer: The value of x is 26
In the given quadrilateral, it is given that, two angles have measurements
And two have measurement
And sum of measurement of angles of a quadrilateral is 360 degree, that is
SO for the given quadrilateral, the value of x is 26 .
Step-by-step explanation:
Answer:
x = 30
Step-by-step explanation:
You want the value of x given that adjacent angles in a parallelogram are (3x+30)° and (2x)°.
Supplementary anglesAdjacent angles in a parallelogram total 180°, so ...
(3x +30)° +2x° = 180°
5x +30 = 180 . . . . . . . . . divide by °, simplify
x +6 = 36 . . . . . . . . . divide by 5
x = 30 . . . . . . . . . subtract 6
The value of x is 30.
__
Additional comment
The angles are (3·30 +30)° = 120°, and 2·30° = 60°.
Related Questions
A translation 5 units right and 6 units down maps A onto A'. Write thetranslation as a vector.
Answers
A translation 5 units right and 6 units down maps A onto A'. Write the
translation as a vector.
we have that
the rule for the translation is
A(x,y) -------> A'(x+5, y-6)What is the equation of the horizontal line that passes through the point (5,-1).X= 5Y=-1Y+1=2(x-5)Y=5x-1
Answers
We have the next point (5,-1) and we need to find the horizontal line that passes through this point.
The equation of a horizontal line with y-intercept b is y = b
Where the point (a,b) = (5,-1)
Hence, the equation of the line is y=-1
The correct answer is the second option.
The owner of a small store buys coats for 40.00 each. She sells the coats for 72.00 each. What percent of the purchase price is the sales price?
Answers
In order to calculathe the percent, we just need to divide the sales price by the purchase price.
So we have:
[tex]\frac{72}{40}=\frac{36}{20}=\frac{18}{10}=1.8=180\text{\%}[/tex]Therefore the sales price represents 180% of the purchase price.
I need help with this. can you help me find the answer please?
Answers
ANSWER
15 degrees Celcius
STEP-BY-STEP EXPLANATION:
From the graph provided in the question tab, you will see that the outdoor temperature is plotted against the number of chips made per 25 seconds by the cricket.
On the x-axis, one box represents 10 units, on the y-axis, one box represents 4 units
At 33 cricket chirps in 25 seconds on the x-axis, we can trace the point to the y-axis, and this will give us 15 degrees Celcius.
Hence, the predicted outdoor temperature is 15 degrees Celcius
how does h (x) =-0.1x-5 change over the interval from x=2 to x=4
Answers
The given expression is,
[tex]h(x)==0.1x-5[/tex]Let us first consider, x = 2. We have,
[tex]h(2)=0.1\times2-5=-4.98[/tex]Now, let us take x = 4, we have,
[tex]h(4)=0.1\times4-5=-4.6[/tex]So the range is, -4.98 to -4.6. So, h (x) decreases by 0.3
Finding the Midpoint of a line SegmentUse this formula to find the Midpoint (mean) of the line segment (-5, -3) and (9,3)
Answers
The formula for determining the midpoint of a line is expressed as
[tex]\begin{gathered} \text{Midpoint = }\lbrack\frac{(x1\text{ + x2)}}{2},\text{ }\frac{(y1\text{ + y2)}}{2}\rbrack \\ \text{From the information given,} \\ x1\text{ = - 5, x2 = 9} \\ y1\text{ = - 3, y2 = 3} \\ \text{Midpoint = }\lbrack\frac{(-\text{ 5 + 9)}}{2},\text{ }\frac{(-\text{ 3 + 3)}}{2}\rbrack \\ \text{Midpoint = (- 2, 0)} \end{gathered}[/tex]
Mrs. Hamilton is trying to plan a party for her math classes and receive two quotes. The Hypotenuse Hall
charges $100 for a damage deposit and $6 per per person for snacks. The Pi Place charges only $20 for a
damage deposit but $10 per person for snacks. Mrs. Hamilton needs your help!
Answers
The hypotenuse hall will be cheaper .
Both places charge $200 for 20 people .
The linear system of equation gives C = 20 + 10 n
Where ,
C = total cost
N = number of cost
What is linear system of equation?A system of linear equations in mathematics is a grouping of one or more linear equations that share the same variables. A collection of one or more linear equations involving the same variables is known in mathematics as a system of linear equations (or linear system). A mathematical representation of a system based on the application of a linear operator is known as a "linear system" in systems theory. Ordinarily, compared to nonlinear systems, linear systems display significantly simpler traits and properties. A line equation is referred to as a linear equation. Or, for example, y + 0.5x 3.5 = 0 and more. The linear equation in each case is the same (remember this!) When two or more linear equations cooperate, this is known as a system of linear equations.
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You invest $275 to start a sandwich stand and decide to charge $5.15 per sandwich.Set up a Linear Model that determines your profit or loss based on the number of sandwiches.How much money will you make if you sell 75 sandwiches?How many sandwiches must you sell to make a $100 profit?
Answers
Let the number of sandwichs sold be "x"
If you charge $5.15 per sandwich then the total sales of the sandwich will be 5.15x
Cost price = $275
The Linear Model that determines your profit or loss based on the number of sandwiches will be expressed as:
[tex]\text{Profit}=\text{Selling price - Cost price}[/tex]Substitute the given parameters;
[tex]\begin{gathered} \text{Profit/Loss}=5.15x\pm275 \\ p(x)=5.15x\pm275 \end{gathered}[/tex]If 75 sandwiches were sold, the amount of money made will be expressed as:
[tex]\begin{gathered} p(75)=5.15(75)-275 \\ p(75)=386.25-275 \\ p(75)=\$111.25 \end{gathered}[/tex]Hence the amount of money made if you sell 75 sandwiches is $111.25
To make $100 profit, the amount of sandwiches must you sell is given as:
[tex]\begin{gathered} 100=5.15x-275 \\ 5.15x=100+275 \\ 5.15x=375 \\ x=\frac{375}{5.15} \\ x\approx72\text{sandwiches} \end{gathered}[/tex]Hence 72 sandwiches must be sold to make a profit of $100
I have a question on area of a triangle an area of a circle. See picture of my problem
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
equilateral triangle:
side = 7x
circle:
radius = 4r
Step 02:
area:
a = circle area - triangle area
triagle area:
triagle area = (b * h) / 2
b = 7x
h:
[tex]\begin{gathered} (7x)^2=h^2+(\frac{7x}{2})^2 \\ 49x^2=h^2+\frac{49x^2}{4} \\ h^2=49x^2-\frac{49x^2}{4}=\frac{147x^2}{4} \\ h\text{ = }\sqrt[]{\frac{147x^2}{4}\text{ }}=6.06x=6.1x \end{gathered}[/tex]h = 6.1x
[tex]\text{triangle area = }\frac{7x\cdot6.1x}{2}=\frac{42.7x^2}{2}=21.35x^2[/tex]circle area:
circle area (r) = π r² = π (4r)² = 16 π r²
a = circle area - triangle area
a = 16 π r² - 21.35x²
The answer is:
a = 16 π r² - 21.35x²
Help me please so i can see if i’m on the rights track. if csc (θ) = 13/12 and 0° < θ < 90°, what is cos (θ)? write the answer in simplified, rationalized form.
Answers
Given in the question is:
[tex]\csc (\theta)=\frac{13}{12}[/tex]Recall the trigonometric identity:
[tex]\csc (\theta)=\frac{1}{\sin (\theta)}[/tex]Therefore, we have that
[tex]\sin (\theta)=\frac{12}{13}[/tex]Recall the trigonometric ratio:
[tex]\begin{gathered} \sin (\theta)=\frac{\text{opp}}{\text{hyp}} \\ \cos (\theta)=\frac{\text{adj}}{\text{hyp}} \end{gathered}[/tex]and, using the Pythagorean Theorem:
[tex]hyp^2=opp^2+adj^2[/tex]From the sin value, we have:
[tex]\begin{gathered} opp=12 \\ hyp=13 \\ \therefore \\ 13^2=12^2+adj^2 \\ 169=144+adj^2 \\ adj^2=169-144=25 \\ adj=\sqrt[]{25} \\ adj=5 \end{gathered}[/tex]Therefore, the value of cos(θ) is:
[tex]\sin (\theta)=\frac{5}{13}[/tex]Part A: On one day, the exchange rate model might be B = 0.60A with the parameter k = 0.60.
Under these conditions, an American tourist exchanging US$ 11 would receive £
Round to the nearest hundredth, if necessary.
Part B: Under those same conditions, an English tourist exchanging £ 11 would receive US$
Round to the nearest hundredth, if necessary.
Answers
The amount of money each tourist will get:
Part A: The American tourist exchanging US$ 11 would receive £6.60.
Part B: The English tourist exchanging £ 11 would receive US$ 18.33.
We are given a relation in terms of algebraic expression:
B = 0.60A
We need to find the money of tourists after exchanging.
Part A:
The American tourist exchanged US$ 11.
substitute the value A = 11 in the given expression, we will get:
B = 0.60 * 11 = 6.60
So, the American tourist will get £6.60.
Part B:
The English tourist exchanged £ 11.
substitute the value B = 11 in the given expression, we will get:
11 = 0.60A
A = 11 / 6.60
A = 18.33333
A = 18.33
So, the English tourist will get US$ 18.33.
Thus, the amount of money each tourist will get:
Part A: The American tourist exchanging US$ 11 would receive £6.60.
Part B: The English tourist exchanging £ 11 would receive US$ 18.33.
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Slope What is the slope of the line through (-4, 2) and (3,-3)?
Answers
We have the next formula in order to obtain the slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where
(-4, 2)=(x1,y1)
(3,-3)=(x2,y2)
we substitute the values
[tex]m=\frac{-3-2}{3+4}=\frac{-5}{7}=-\frac{5}{7}[/tex]the slope is -5/7
Let s be an Integer. Alonso claims that -s must always be less than zero. Iliana claims that -s is only sometimes less than zero. Whose statement is correct? Explain, support your reasoning with an example
Answers
Answer:
Iliana's claim is correct
Explanation:
If s is an integer.
Integers are positive or negative whole numbers.
• Illiana's claim is correct.
This is as a result of the fact that when s is negative: e,g s=-5
[tex]\begin{gathered} s=-5 \\ -s=-(-5)=5 \\ 5\text{ is greater than 0} \end{gathered}[/tex]However, when s is a positive integer:
[tex]\begin{gathered} s=5 \\ -s=-5 \\ -5\text{ is less than 0} \end{gathered}[/tex]Therefore, for an integer s, -s is only sometimes less than zero.
Illiana's claim is correct.
how do you think you can represent the number 2300 as a number times a multiple of 10? How do you think you can represent the number 2300 as a number x 10 to some exponents? How could you describe the relationship between the two representations?
Answers
Answer
23 × 10 = 2300
2.17¹⁰ = 2300
Explanation
The first parts us to represent 2300 as a number (let that number be x) multiplied by 10
x × 10 = 2300
10x = 2300
Divide both sides by 10
(10x/10) = (2300/10)
x = 230
The second part asks us to represent 2300 as a number (let that number be y) raised to power 10
y¹⁰ = 2300
To solve for y, we will take the logartihms of both sides
Log (y¹⁰) = Log 2300
10 log y = log 2300
Divide both sides by 10
(10 log y)/10 = (log 2300)/10
Log y = (3.362/10)
Log y = 0.3362
We will now take the Antilog of both sides
y = 2.17
Hope this Helps!!!
4. Principal Sanders wants to know if wearing school uniforms will help students improve theirmath test scores. She decides to conduct an experiment to find out She chooses two groups ofstudents to test One group will wear uniforms, the other will not.Part A. Define the variables and treatment for the experiment. (3 points)I1 What is the control variable? Why?
Answers
Note that:
The control variable is the variable that does not change (that is, constant ) in an experiment. It does not take part in the experiment
The response variable is the dependent variable that determines the outcome of the experiment.
The treatment of an experiment is the independent variable, and it determines the outcome of the experiment.
From the illustration given in this exercise, the control variable, the response variable, and the treatments are identified below with reasons.
1) The control variable = The mathematical abilities of the students
Reason: The students chosen for the experiment must have the same mathematical abilities to prevent bias in the results of the experiment.
2) The response variable = Math test scores
Reason: The maths test scores of the two groups of students are the outcomes of the experiment, hence the response variable.
3) The treatment for the experiment = Wearing of school uniforms
Reason: Wearing of school uniforms is the treatment that the two groups of students were subjected to in order to confirm if their will be any effects on their Maths test scores.
A) If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is: B) If half of the passengers are men, find the probability that the mean height of the men is less than 74 in. C) When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? D) When considering the comfort and safety of passengers, why are women ignored in this case?
Answers
Hello there. To solve this question, we'll have to remember some properties about probabilities.
Selecting male passengers randomly from the 400 passengers set, we want to find the probability that he can fit through the 74 in doorway without bending.
First, calling x the height of the random selected man, the probability of him fitting is P(x <= 74), and of him not fitting is P(x > 74)
To find P(x <= 74), we calculate the z-score by the formula:
[tex]z=\frac{x-\mu}{\sigma}=\frac{74-69}{2.8}=\frac{5}{2.8}\approx1.78[/tex]Looking for a table of z-scores for a normally distributed set, we say that the probability is around 95 or 96%. Using the under 8 approximation, P(x <= 74) = 0.96246 or 96.25%.
part (b)
We now have that the sample size is 200, since we had 400 passengers on the flight.
Making the new standard deviation as:
[tex]s=\frac{\sigma}{\sqrt[]{\text{sample}}}=\frac{2.8}{\sqrt[]{200}}=0.198[/tex]From the Central limit theorem, the z-score will then be:
z = (74 - 69)/0.198 = 25.25
it says, "or use prime factorization" #1-3, and 5 pls!!
Answers
The LCM (lowest common multiple) of the following;
(1) 5 and 7
5 = 1 x 5
7 = 1 x 7
LCM = 1 x 5 x 7
LCM = 35
(2) 4, 5 and 10
4 = 2 x 2
5 = 1 x 5
10 = 2 x 5
LCM = 2 x 2 x 5
LCM = 20
(3) 6, 9 and 12
6 = 2 x 3
9 = 3 x 3
12 = 2 x 2 x 3
LCM = 2 x 2 x 3 x 3
LCM = 36
Find the LCD (lowest common denominator) of the fractions,
[tex]\begin{gathered} \frac{3}{8},\frac{3}{5} \\ We\text{ take the LCM of the denominators, that is 8 and 5} \\ \text{The LCM is,} \\ 5=1\times5 \\ 8=2\times2\times2 \\ \text{LCM}=2\times2\times2\times5 \\ \text{LCM}=40 \\ \text{The fractions can now be re-written as } \\ \frac{15}{40}\text{ and }\frac{24}{40} \end{gathered}[/tex]The weighted voting systems for the voters A, B, C, ... are given in the form q: w1, w2, w3, w4, ..., wn. The weight of voter A is w1, the weight of voter B is w2, the weight of voter C is w3, and so on.Calculate, if possible, the Banzhaf power index for each voter. Round to the nearest hundredth. (If not possible, enter IMPOSSIBLE.){72: 46, 35, 22, 14}
Answers
I would not be able to continue this session, because the information is incomplete. Thank you.
I solved part C I just need help with part D
Answers
1) Gathering the data
8% sales tax
2 DVDs' price: $21.60 (after taxation)
2) To find out how much for the DVDs without the sales tax, let's write this equation.
P for the price without tax, 1.08 the sales tax factor, $21.60 the full price
p (1.08) =21.60 Let's divide both sides by 1.08
p= 21.60 /1.08
p= 20
3) So the price without tax, is $20
Solve the equation 2(8+4c)=32
Answers
c = 2
Explanation:
2(8+4c)=32
we open the bracket:
2×8 + 2×4c = 32
16 + 8c = 32
collect like terms:
8c = 32 - 16
8c = 16
Divide through by 8:
8c/8 = 16/8
c = 2
4
Ellie goes to tutoring every 4 days for math
and every 12 days for Science. If Ellie
attended tutoring for both Math and Science
today, when is the next time she will attend
both sessions on the same day?
Answers
Answer:
gcm conditions
1. all numbers are entered (in the picture, enter numbers 2 and 3)
2. if there are the same number, take the number that has the largest power
ahe Will attend both sessions 12 days after today
A cyclist pedals at a rate of 300 m min(exponent of -1) for 20 minutes. Then she slows down to 150 m min (exponent of -1) for 16 minutes, then races at 400 m min (exponent -1) for four minutes. find the distance traveled after20 minutes36 minutes40 minutesWrite a piecewise linear function for the distance of D(t) in terms of time (T) in minutes. find the distance traveled after 30 minutes38 minutesbonus - when has the cyclist traveled? 8km9 km
Answers
Given:
A cyclist pedals at a rate of 300 m min(exponent of -1) for 20 minutes. Then she slows down to 150 m min (exponent of -1) for 16 minutes, then races at 400 m min (exponent -1) for four minutes.
We will draw the diagram between the rate (speed of the cyclist) and the time (t) in minutes, the graph will be as follows:
For the first 20 minutes, the rate increased from 0 to 300 m/min
Then the next 16 minutes, the rate decreased to 150 m/min
And in the last 4 minutes, the rate increased to 400 m/min.
To find the distance traveled, we will find the area under the lines according to a specific time.
So, first, we will find the distance traveled after 20 minutes
It will be as follows = d(20)
[tex]d(20)=\frac{1}{2}*300*20=3000\text{ }m=3\text{ }km[/tex]And the distance traveled from 20 min to 36 min is the area of a trapezoid with a height = 16 min. and the parallel base are 150 and 300
So, the area will be =
[tex]\frac{1}{2}(300+150)*16=3600\text{ }m=3.6\text{ }km[/tex]So, the distance traveled after 36 minutes = 3 + 3.6 = 6.6 km
And the distance traveled from 36 min to 40 min is the area of a trapezoid with a height = 4 min. and the parallel bases are 150 and 400
So, the area =
[tex]\frac{1}{2}(150+400)*4=1100\text{ }m=1.1\text{ }km[/tex]So, the total distance after 40 minutes = 6.6 + 1.1 = 7.7 km.
=========================================================
To find the piecewise linear function for the distance of D(t) in terms of time (T) in minutes.
First, we will write the function v(t) that represents the rate from the graph.
[tex]v(t)=\begin{cases}{15t\rightarrow0\leq t\leq20} \\ -9.375t+487.5\rightarrow20\leq t\leq36 \\ {62.5t-2100\rightarrow t\ge36}\end{cases}[/tex]To find the function of the distance integrate each function with respect to the time t:
[tex]D(t)=\begin{cases}{7.5t^2}\rightarrow0\leq t\leq20 \\ {-4.6875t^2+487.5t-4875\rightarrow20\leq t\leq36} \\ {31.25t^2-2100t+41700\rightarrow t\ge36}\end{cases}[/tex]у = 3х – 7у = 3х + 1Are these equations, parallel, perpendicular or neither
Answers
A line equation can be written in slope-intercept form, which is
[tex]y=mx+b[/tex]Where m represents the slope and b represents the y-intercept.
If the slopes of two lines are equal they are parallel, if one slope is minus the inverse of the other they are perpendicular, otherwise they are neither.
Comparing our lines to the slope-intercept form, we can find their slopes.
[tex]\begin{gathered} y=3x-7\Rightarrow m=3 \\ y=3x+1\Rightarrow m=3 \end{gathered}[/tex]Since their slopes are equal, those lines are parallel to each other.
A road crew Musri pave a road that is 7/8 miles long they can repave 1/56 miles each hour how long will it take the crew to repave the road
Answers
Given data :
[tex]1\text{ hour = }\frac{1}{56}miles[/tex]distance required to cover =
[tex]\frac{7}{8}[/tex]thus, the time taken is,
[tex]\begin{gathered} =\frac{\frac{7}{8}}{\frac{1}{56}} \\ =\frac{7}{8}\times56 \\ =\frac{7}{1}\times7 \\ =7\times7 \\ =49 \end{gathered}[/tex]thus the time taken is 49 hours.
The length of a rectangle is 2ft more than twice the width. The area is 144 ft squared. Find the length and width of the rectangle.
Answers
The formula for the area of a rectangle (A) is given as
[tex]A=\text{length}\times breadth[/tex]Given that
The length of a rectangle is 2ft more than twice the width,
Therefore,
length = 2 + 2width
where,
[tex]\begin{gathered} w=\text{width} \\ l=2+2w \\ A=144ft^2 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 144=(2+2w)\times w \\ 144=2w+2w^2 \\ 144=2(w+w^2) \\ \frac{144}{2}=\frac{2(w+w^2)}{2} \\ 72=w+w^2 \\ w^2+w-72=0 \end{gathered}[/tex]Factorizing the equation above
[tex]\begin{gathered} w^2+9w-8w-72=0 \\ w(w+9)-8(w+9)=0 \\ (w-8)(w+9)=0 \\ w-8=0\text{ or }w+9=0 \\ w=8\text{ or w=-9} \\ \therefore w=8or-9 \end{gathered}[/tex]Note that the width can never be negative, therefore the width of the rectangle is 8.
Recall that:
[tex]\begin{gathered} l=2_{}+2w=2+2(8)=2+16=18 \\ l=18 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \text{length = 18ft} \\ \text{width = 8ft} \end{gathered}[/tex]
Find the population mean or sample mean as indicated.Sample: 24, 8, 9, 5, 19
Answers
The mean of a population set can be calculated through the formula:
[tex]\bar{x}=\frac{\sum ^n_{i\mathop=1}(x_i)}{n}[/tex]in which, n is the total number of data points that are in the set
then, with the sample given the mean can be found as,
[tex]\begin{gathered} \bar{x}=\frac{24+8+9+5+19}{5} \\ \bar{x}=\frac{65}{5} \\ \bar{x}=13 \end{gathered}[/tex]Answer:
The sample mean is 13.
2. For each of the next dot plots, guess the approximate location of the mean by thinking aboutwhere the balance point for the data would be. Then check how close your guess was bycalculating the mean.0 1 2 3 4 5 6 7 8 9 1001235 6 7 89 10012569 10
Answers
ANSWER
1) The plot looks like the fulcrum would balance at point 4
After calculation, the mean is 4.
2) The plot looks like the fulcrum would balance at point 3;
After calculation, the mean is 3.8.
3) The plot looks like the fulcrum would balance at point 8;
After calculation, the mean is 7.2
EXPLANATION
From the given data;
1) The plot looks like the fulcrum would balance at point 4.
the mean
[tex]\begin{gathered} mean(x)=\frac{(2+2+2)+(7+7)}{5} \\ =\frac{20}{5} \\ =4 \end{gathered}[/tex]2) The plot looks like the fulcrum would balance at point 2;
The mean;
[tex]\begin{gathered} x=\frac{0+1+1+2+2+2+3+3+4+10}{10} \\ =\frac{38}{10} \\ =3.8 \end{gathered}[/tex]3) The plot looks like the fulcrum would balance at point 8;
[tex]\begin{gathered} x=\frac{0+6+7+7+8+8+8+9+9+10}{10} \\ =\frac{72}{10} \\ =7.2 \end{gathered}[/tex]Write an equation for the line that passes through the point (2,2) and is perpendicular to -8x+y=8. Use slope-intercept form.
Answers
Ok, first of all, let's put the equation of the line in the slope-intercept form:
-8x+y=8
y=8x+8
The slope of this line is m=8.
The slope of a perpendicular line is the negative reciprocal of the slope of the first line, so:
m2=-1/8
Now let's calculate the equation of the perpendicular linbe, using the given point, (2,2):
y-y1=m*(x-x1)
y-2 = -1/8(x-2)
y-2=-1/8x + 2/8
y=-1/8x +2/8 +16/8
y=-1/8x + 18/8
y= -1/8x + 9/4
The equation will be y= -1/8x + 9/4
Find the z-score for 67.4% of the distribution area to the right
Answers
Usually, the tables for z-scores report the value at the left of given z-values. Then we can rewrite the question.
When the z-value has 67.4% of the area distribution it means that at its left we have: 100% - 67.4% = 32.6% of the area.
Now we just need to read the z-value table and find the z-score associated with a probability of 0.326. Reading from the table, the z value is approximately -0.45.
The mean number of employee sick days used per week at a company is 6.4 with a standard deviation of 1.5 days. What proportion of weeks would you expect to have more than 7 employee sick days used?
Answers
Given the z-score formula,
[tex]\begin{gathered} z=\frac{x-\mu}{\sigma} \\ \text{Where x =7} \\ \mu=6.4\text{ and} \\ \sigma=1.5 \\ z=\frac{7-6.4}{1.5}=\frac{0.6}{1.5}=0.4 \end{gathered}[/tex]Given the z-score of 0.4